CBSE Class 10 Mathematics Probability Worksheet Set A

Read and download free pdf of CBSE Class 10 Mathematics Probability Worksheet Set A. Students and teachers of Class 10 Mathematics can get free printable Worksheets for Class 10 Mathematics Chapter 15 Probability in PDF format prepared as per the latest syllabus and examination pattern in your schools. Class 10 students should practice questions and answers given here for Mathematics in Class 10 which will help them to improve your knowledge of all important chapters and its topics. Students should also download free pdf of Class 10 Mathematics Worksheets prepared by school teachers as per the latest NCERT, CBSE, KVS books and syllabus issued this academic year and solve important problems with solutions on daily basis to get more score in school exams and tests

Worksheet for Class 10 Mathematics Chapter 15 Probability

Class 10 Mathematics students should refer to the following printable worksheet in Pdf for Chapter 15 Probability in Class 10. This test paper with questions and answers for Class 10 will be very useful for exams and help you to score good marks

Class 10 Mathematics Worksheet for Chapter 15 Probability

Question. A letter is chosen at random from the word ‘ASSASSINATION’. The probability that it is a vowel is

a. 6/13

b. 7/13

c. 6/31

d. 3/13

Answer : a. 6/13

Explanation: Vowels present in the given word are A, A, I, A, I, O = 6

Number of possible outcomes = {A, A, I, A, I, O} = 6

Number of total outcomes = 13

Required Probability = 6/13

Question. A number ‘x’ is chosen at random from the numbers -4, -3, -2, -1, 0, 1, 2, 3, 4, 5. The probability that ׀x|< 3 is

a. 1

b. 0

c. 1/2

d. 7/10

Answer : c. 1/2

Explanation: Number of total outcomes = 10 {-2,-1,0,1,2} =5

Number of possible outcomes = = 5

Required Probability = 5/10=1/2

Question. An unbiased die is thrown once. The probability of getting an odd number is

a. 1/3

b. 1/2

c. 2/5

d. 2/3

Answer : b. 1/2

Explanation: Number of odd numbers on a dice = {1, 3, 5}, = 3

Number of possible outcomes = 3

Number of Total outcomes = 6

Required Probability 3/6 =1/2

Question. A lot consists of 40 mobile phones of which 32 are good, 3 have only minor defects and 5 have major defects. Ram will buy a phone if it is good or have minor defects.One phone is selected at random. The probability that it is acceptable to Ram is___.

a. 3/40

b. 4/5

c. 3/5

d. 7/8

Answer : d. 7/8

Explanation: Number of phones which are good and minor defects = 32 + 3 = 35

Number of possible outcomes = 35

Number of Total outcomes = 40

Required Probability =35/40=7/8

Question. A black dice and a white dice are thrown at the same time. Write all the possible outcomes. What is the probability that the difference of the numbers appearing on the top of the two dice is 2?
Answer : Consider the set of ordered pairs

{(1,1)(1,2)(1,3)(1,4)(1,5)(1,6)

(2,1)(2,2)(2,3)(2,4)(2,5)(2,6)

(3,1)(3,2)(3,3)(3,4)(3,5)(3,6)

(4,1)(4,2)(4,3)(4,4)(4,5)(4,6)

(5,1)(5,2)(5,3)(5,4)(5,5)(5,6)

(6,1)(6,2)(6,3)(6,4)(6,5)(6,6)}

Clearly, there are 36 elementary events.

∴n(Total number of throws) = 36

number of pairs such that difference of the numbers appearing on top of the two dice is 2 can be selected as listed below:

{(1,3)(2,4)(3,1)(3,5)(4,2)(4,6)(5,3)(6,4)}

Therefore, n(Favourable events) = 8

P(difference of the number is 2) = (Number of pairs such that difference of the numbers Appearing on the top of the two dice is 2) / (Total number of throws)
=8/36=2/9

Question. Three unbiased coins are tossed together. Find the probability of getting at least two heads?

Answer : If any of the elementary events HHH, HHT, HTH, and THH is an outcome, then we say that the event "Getting at least two heads" occurs.

Favourable number of elementary events = 4

total no. of possible events when three coins are tossed = 8

Hence, required probability =4/8=1/2

Question. Two dice are thrown simultaneously. Find the probability of getting a multiple of 2 on one dice and a multiple of 3 on the other.

Answer : Two dice are thrown simultaneously. We have to find the probability of getting a multiple of 2 on one dice and a multiple of 3 on the other.

Let A be the event of getting a multiple of 2 on one die and a multiple of 3 on the other.

Then, the elementary events favourable to A are:

(2, 3), (2, 6), (4, 3), (4, 6), (6, 3), (6, 6), (3, 2), (3, 4),

(3, 6), (6, 2), (6, 4). Favourable number of elementary events =11

Hence, required probability 11/36

Question. A bag contains lemon flavoured candies only. Malini takes out one candy without looking into the bag. What is the probability that she takes out?

i. an orange flavoured candy?

ii. a lemon flavoured candy?

Answer : i. The probability that she takes out an orange flavoured candy is 0 because the bag contains lemon flavoured candies only.

ii. Probability that she takes out a lemon flavoured candy is 1 because the bag contains lemon flavoured candies only.

Question. Cards marked with numbers 5 to 50 are placed in a box and mixed thoroughly. A card is drawn from the box at random. Find the probability that the number on the taken out card is

i. a prime number less than 10

ii. a number which is a perfect square.

Answer : According to question we are given that Cards marked with numbers 5 to 50 are placed in a box and mixed thoroughly. A card is drawn from the box at random.

Therefore All possible outcomes are 5, 6, 7, 8 …………… 50.

Number of all possible outcomes = 46

i. Out of the given numbers, the prime numbers less than 10 are 5 and 7.

Suppose E1 be the event of getting a prime number less than 10.

Then, number of favorable outcomes = 2

Therefore, P(getting a prime number less than 10) = P(E) = 2/46 = 1/23

ii. Out of the given numbers, the perfect squares are 9, 16, 25, 36 and 49.

Suppose E2 be the event of getting a perfect square.

Then, number of favorable outcomes = 5

Therefore, P(getting a perfect square) = P(E) = 5/46

Question. A bag contains 5 black, 7 red and 3 white balls. A ball is drawn from the bag at random. Find the probability that the ball drawn is(i) red (ii) black or white (iii) not black.
Answer : Proabibilty of the event = Number of favourable outcomes / Total Number of possible outcomes
Total number of balls = 5 + 7 + 3 = 15
i. Number of red balls = 7
P(drawing a red ball) = 7/15
ii. Number of black or white balls = 5 + 3 = 8
P(drawing a black or white ball) = 8/15
iii. Number of balls which are not black = 15 - 5=10
P(drawing a ball that is not black) = 10/15 = 2/5
Hence, the probability of getting a red ball, a black or white ball and a not black
ball are 7/15. 8/15 and 2/3 respectively.

Question. Why is tossing a coin considered as the way of deciding which team should get the ball at the beginning of a football match?
Answer : Proabibilty of the event = Number of favourable outcomes / Total Number of possible outcomes
Probability of head= P(H) = 1/2
Probability of tail = P(T) = 1/2
i.e. P (H) = 1/2 = P (T) = 1/2
Probability of getting head and tail both are same.
Tossing a coin considered to be fairway.

Question. Two dice are thrown simultaneously. Find the probability of getting a multiple of 2 on one dice and a multiple of 3 on the other.
Answer : Two dice are thrown simultaneously. We have to find the probability of getting a multiple of 2 on one dice and a multiple of 3 on the other.
Let A be the event of getting a multiple of 2 on one die and a multiple of 3 on the other.
Then, the elementary events favourable to A are:
(2, 3), (2, 6), (4, 3), (4, 6), (6, 3), (6, 6), (3, 2), (3, 4),
(3, 6), (6, 2), (6, 4). Favourable number of elementary events =11
Hence, required probability = 11/36

Question. In a simultaneous throw of a pair of dice, find the probability of getting a number other than 5 on any dice.
Answer : Favourable outcomes of a number other than 5 on any dice =
{(1,1)(1,2)(1,3)(1,4)(1,6)
(2,1)(2,2)(2,3)(2,4)(2,6)
(3,1)(3,2)(3,3)(3,4)(3,6)
(4,1)(4,2)(4,3)(4,4)(4,6)
(6,1)(6,2)(6,3)(6,4)(6,6)}
Therefore, favourable number of cases to the event = 25
∴ Probability of a number other than 5 on any dice = Number of favourable outcomes / Number of total outcomes = 25/36

Question. Two coins are tossed together. Find the probability of getting both heads or both tails.
Answer : Two coins are tossed together.
Possibilities are HH, HT, TH, TT
Total outcomes = 4
Both heads or both tails = HH, TT
Number of favourable outcome = 2
Probability = Number of favourable outcomes / Total Number of outcomes
P(HH or TT) = 2/4 = 1/2

Question. Cards numbered 11 to 60 are kept in a box. If a card is drawn at random from the box, find the probability that the number on the drawn card is (i) an odd number, (ii) a perfect square number, (iii) divisible by 5, (iv) a prime number less than 20.
Answer : According to the question,
All possible outcomes are 11. 12. 13,....... 60
Total number of possible outcomes = (60 - 10) = 50
i. Suppose, E₁ be the event that the number on the drawn card is an odd number.
⇒ the favourable outcomes are 11. 13. 15,....... 59
Clearly, these numbers form an AP with a = 11 and d = 2.
T_n = 59 ⇒ 11 + (n - 1) x 2 = 59 ⇒ (n - 1) x 2 = 48 ⇒ n - 1 = 24 ⇒ n = 25
So, the number of favourable outcomes = 25
∴ P(getting an odd number) = P (E₁) = 25/50 = 1/2 .
ii. Suppose, E₂ be the event that the number on the drawn card is a perfect square number.
⇒ the favourable outcomes are . 16. 25. 36. 49..
The number of favourable outcomes = 4.
∴ P(getting a perfect square number) P (E₂) = 4/50 = 2/25 ..
iii. Suppose, E₃ be the event that the number on the drawn card is divisible by 5.
⇒ the favourable outcomes are 15, 20. 25..........60
Clearly, these numbers form an AP with a = 15 and d=5.
Tm = 60 ⇒ 15 + (m - 1) x 5 = 60 ⇒ (m - 1) x 5 = 45 ⇒ m - 1 = 19 ⇒ m = 10
So, the number of favourable outcomes = 10
∴ P(getting a number divisible by 5) = P (E₃) = 10/50 = 1/5
iv. Suppose, E₄ be the event that the number on the drawn card is a prime number less than 20.
⇒ the favourable outcomes are 11, 13, 17, 19
So, the number of favourable outcomes = 4
∴ P(getting a prime number less than 20) = P (E₄) = 4/50 = 2/25

Question. A bag contains, white, black and red balls only. A ball is drawn at random from the bag. If the probability of getting a white ball is 3/10 and that of a black ball is , 2/5 then find the probability of getting a red ball. If the bag contains 20 black balls, then find the total number of balls in the bag.
Answer : P (White ball) = 3/10
P(Black ball) = 2/5
P(E) = 1 - P( not E)
Probability of not getting white and black ball is equals to probability of getting red balls.
P(Red ball) = 1 - (3/10 + 2/5) = 3/10
2/5 x Total no of balls = 20 (red balls)
Hence, Total numbers of balls = 20x5/2 = 50

Question. The probability of selecting a red ball at random from a jar that contains only red, blue and orange balls is . The probability of selecting a blue ball at random from the same jar is . If the jar contains 10 orange balls, find the total number of ball in the jar.
Answer : P(red ball) = 1/4, P(blue ball) = 1/3
P(orange ball) = 1 - 1/4 - 1/3 = 5/12
Suppose total no. of balls = x
Then 10/x = 5/12
Hence x = 24

Question. All red face cards are removed from a pack of playing cards. The remaining cards are well-shuffled and then a card is drawn at random from them. Find the probability that the drawn card is
i. a red card,
ii. a face card,
iii. a card of clubs.
Answer : There are 6 red face cards. These are removed.
Thus, remaining number of card = 52 – 6 = 46.
i. Number of red cards now = 26 – 6 = 20.
Therefore, P(getting a red card) = Number of favourable outcomes / Number of all possible outcomes = 20/46 = 10/23
Thus, the probability that the drawn card is a red card is 10/23.
ii. Number of face cards now = 12 – 6 = 6.
Therefore, P(getting a face card) = Number of favourable outcomes / Number of all possible outcomes = 6/46 = 3/23
Thus, the probability that the drawn card is a face card is 3/23.
iii. The number of card of clubs = 12.
Therefore, P(getting a card of clubs) = Number of favourable outcomes / Number of all possible outcomes = 12/46 = 6/23
Thus, the probability that the drawn card is a card of clubs is 6/23

Question. A box contains cards bearing numbers 6 to 70. If one cards is drawn at random from the box, find the probability that it bears
i. a one digit number.
ii. a number divisible by 5,
iii. an odd number less than 30,
Answer : i. Let E be the event of getting a one digit number.
Number of possible outcomes = 70 - 6 + 1 = 65
The outcomes favourable to E are 6,7,8 and 9
Number of favourable outcomes = 4
P(E)=P(Getting a one digit number) = 4/65
ii. Let F be the event of getting a number divisible by 5.
Number of possible outcomes =65
The outcomes favourable to the event F are 10,15,20,...., 65,70.
Number of outcomes favourable to F = 13
P(F)=P(Getting a number divisible by 5) = 13/65 = 1/5
iii. Let G be the event of getting an odd number less than 30.
Number of possible outcomes =65
The outcomes favourable to the event G are 7,9,11,13,....., 29.
Number of favourable outcome =12
P(G)=P(Getting an odd number less than 30) = 12/65

Question. A box contains 90 discs which are numbered 1 to 90. If one disc is drawn at random from the box, find the probability that it bears
i. a two digit number,
ii. number divisible by 5.
Answer : 20. No. of all possible outcomes = 90
i. Discs with two digit number are 10 to 90
No. of discs with two digits numbers = 90 - 10 +1 = 81
∴ No of favourable outcomes = 81
P(a disc with two digit number) = No of favourable outcome / No of all possible outcome = 81/90 = 9/10
ii. The numbers having 0 or 5 at its once place are divisible by 5 = 5,10,15.....90
Total no. of favourable outcomes = 18
P(a disc with a number divisible by 5) = 18/90 = 1/5

Question. A card is drawn at random from a well shuffled deck of 52 cards. The probability that it will be a spade or a king is

a. 4/13

b. 6/13

c. 8/13

d. 10/13

Answer : A

Explanation: Number of spades = 13

Number of kings = 3 (one spade king is counted in No. of spades)

Number of possible outcomes = 13 + 3 = 16

Number of Total outcomes = 52

Required Probability =16/52=4/13

Question. The probability of an impossible event is

a. 0.01

b. 100

c. zero

d. 1

Answer : C

Explanation: An event which has no chance of occurrence is called an impossible event.

for example: The probability of getting more than 6 when a die is thrown is an impossible event because the highest number in a die is 6

The probability of an impossible event is always zero.(0)

Question. The probability that a leap year will have 53 Sundays or 53 Mondays is

a.4/7

b.2/7

c.1/7

d.3/7

Answer : D

Explanation: Leap year contains 366 days = 52 weeks + 2 days 52 weeks contain 52 Sundays and 52 weeks contain 52 Mondays

We will get 53 Sundays or 53 Mondays if one of the remaining two days is a Sunday or Monday Total possibilities for two days are:

(Sunday, Monday), (Monday, Tuesday), (Tuesday, Wednesday), (Wednesday,Thursday), (Thursday, Friday), (Friday, Saturday), (Saturday, Sunday)

Number of Total possible outcomes = 7

Number of possible outcomes either Sunday or Monday or Both = 3

Required Probability = 3/7

Question. Cards marked with numbers 1, 2, 3, ……….., 25 are placed in a box and mixed thoroughly and one card is drawn at random from the box. The probability that the number on the card is a multiple of 3 and 5 is
a. 12/25
b. 4/25
c. 1/25
d. 8/25

Answer : C
Explanation: Multiples of 3 = 3 6 9 12 15 18 21 24
Multiples of 5 = 5 10 15 20 25
Number of possible outcomes (multiple of 3 and 5) = {15} = 1
Number of Total outcomes = 25
∴ Required Probability =1/25

Question. A game of chance consists of spinning an arrow which comes to rest pointing at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 and these values are equally likely outcomes. The probability that it will point at a number greater than 5 is
a. 1/2
b.1/4
c.1/5
d.1/3

Answer : A
Explanation: Number of possible outcomes = {6, 7, 8, 9, 10} = 5
Number of total outcomes = 10
∴ Required Probability = 5/10 =1/2

Very Short Answer type Questions

Question. The probability of selecting a rotten apple randomly from a heap of 900 apples is 0.18. What is the number of rotten apples in the heap.
Answer : 162

Question. A bag contains cards which are numbered from 2 to 90. A card is drawn at random from the bag. Find the probability that it bears a two digit number
Answer : 𝟖𝟏/𝟖𝟗

Question. The Probability of guessing the right answer to a certain question in a test is 𝑥/12 . If the probability of not guessing the correct answer to this question is 2/3 , then find value of x
Answer : 4

Question. A card is drawn from a pack of 52 cards. Find the probability of getting a king of red colour
Answer : 𝟏/𝟐𝟔

Question. Two coins are tossed simultaneously. Find the probability of getting at most one head
Answer : 𝟑/𝟒

Question. A bag contains 40 balls out of which some are red, some are blue and remaining are black. If the probability of drawing a red ball is 11/20 and that of blue ball is 1/5 , then what is the no. of black balls?
Answer : 10

Question. A card is drawn from a pack of 52 cards. Find the probability that the card drawn is not a face card
Answer : 𝟏𝟎/𝟏𝟑

Question. A card is drawn from a well shuffled deck of cards. What is the probability that the card drawn is neither a king nor a queen?
Answer : 11/13

Question. A die is thrown twice. Find the probability of getting a sum less than 8
Answer : 𝟕/𝟏𝟐

Question. A box contains cards numbered 6 to 50. A card is drawn at random from the box. Find the probability that the card drawn has a number which is a perfect square
Answer : 𝟏/𝟗

Question. A bag contains cards numbered from 1 to 49. After mixing the cards thoroughly a card is drawn from the bag at random, Find the probability that the number on the drawn card is an odd number
Answer : 25/49

Question. A month is selected at random in a year. Find the probability that it is March or October.
Answer : 1/6

Question. A number is selected from first 50 natural numbers. What is the probability that it is a multiple of 3 or 5?
Answer : 𝟐𝟑/𝟓𝟎

Question. A card is drawn at random from a well-shuffled pack of 52 cards. Find the probability that the drawn card is neither a king nor a queen.

Answer : Total number of cards = 52.

Total number of kings and queens = 4+4 = 8.

Remaining number of cards = 52 - 8 = 44.

P(getting a card which is neither a king nor a queen) =44/52 =11/13

Question. Two unbiased dice are thrown. Find the probability that the total of the numbers on the dice is greater than 10.

Answer : We know that ,When a pair of dice is thrown, the total number of possible outcomes are 36.

Favourable outcomes of the sum greater than 10 = {(5,6)(6,5)(6,6)}

Therefore, number of cases favourable to the event=3

Hence, Probability of getting the sum greater than 10 = 3/36=1/12

More Question-

Question. Two dice are thrown together. Find the probability that the product of the numbers on the top of the dice is
a) 6
b) 12
c) 7
Answer : (1/9, 1/9, 0)

Question. Two different dice are thrown at the same time. Find the probability that the sum of the two numbers appearing On the top of the dice is 7
Answer : (1/6)

3. A pair of dice is tossed once, find the probability of getting
a) a total of 2
b) a total of 5
c) an even number as the sum
d) same number on each dice
Answer : (1/36)
(1/9)
(1/2)
(1/6)

4. A die is thrown once. Find the probability of getting the following:
a) a prime number
b) a number lying between 2 and 5
Answer : (1/2)
(1/3)

Question. A card is drawn at random from a well shuffled pack of playing cards. Find the probability of getting a red face card
Answer : (3/26)

Question. One card is drwn from a well shuffled deck of 52 playing cards. Find the number of probability of getting
a) A face card
b) A black queen or a red king
c) a king of red colour
d) the jack of hearts
e) a spade.
f) either a king or a queen
g) neither a king nor a queen
Answer : (3/13)
(1/13)
(1/26)
(1/52)
(1/4)
(2/13)
(11/13)

Question. From a pack of 52 playing cards, Jacks, Queens, Kings and Aces of red colour are removed. From the remaining,
A card is drawn at random. Find the probability that the card drawn is
a) A black queen
b) A non – face card
c) A black jack
d) a Black King or a Red Queen
Answer : (1/21)
(10/13)
(1/22)
(1/13)

Question. A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball from the bag is thrice that of red ball, find the number of blue balls in the bag
Answer : (15)

Question. A bag contains 6 red, 3 black and 6white balls. A ball is selected at random from the bag. Find the probability that the selected ball is
a )Red or black b) not black
Answer : (3/5, 4/5)

Question. Cards marked with numbers 5,6,7,………………………..74 are placed in a bag and mixed thoroughly. One card is Drawn at random from the bag. Find the probability that the number on the card is a perfect square
Answer : (3/35)

Question. Cards numbered 2,3, 4, 5, 6, -------,49 are put in a box and mixed thoroughly. If one card is drawn at random Find the probability that the number on the card is
a) Even number
b) prime number
c) Divisible by 6
d) A perfect square
Answer : (1/2)
(5/16)
(1/6)
(1/8)

Question. Two unbiased coins are tossed. Calculate the probability of getting
a) Exactly two heads
b) At least two tails
c) At most two tails
Answer : (1/4)
(1/4)
(3/4)

Question. A letter is chosen at random from the English alphabet. Find the probability that the letter chosen
a) Is a vowel
b) Is a consonant
c) Follow r
Answer : (5/26)
(21/26)
(8/26)

Question. Find the probability of 53 Sundays in the year 2012
Answer : (2/7)

Question. Which of the following cannot be the probability of an event?
a) 1/5
b) 0.3
c) 4%
d) 5/4

Question. A card is drawn from a pack of 52 playing cards. The probability of getting a face card is
a) 3/13
b) 4/13
c) ½
d) 2/3

Question. The probability of drawing a red queen from a well shuffled deck of 52 cards is
a) 1/13
b) 2/13
c) 1/26
d) 1/52

Question. A die is thrown, the probability of getting a number less than 3 and greater than 2 is
a) 0
b) 1
c) 1/3
d) 2/3

Question. A card is drawn from a well – shuffled deck of 52 playing cards. The probability that it is not a face card is
a) 12/52
b) 16/52
c) 10/13
d) 9/13

Question. If an event cannot occur then its probability of occurring is
a) 1
b) 2/3
c) ½
d) 0

Question. The probability of getting a perfect square number from the numbers 1 to 10 is
a) 3/10
b) ½
c) 2/5
d) 1/5

Question. The probability of throwing a number less than 6 with a fair die is
a) 5/6
b) 1
c) 1/6
d) 2/3

Q.- What is the probability that a leap year,selected at random will contain 53 Sundays ?

Sol. Number of days in a leap year = 366 days

Now, 366 days = 52 weeks and 2 days

The remaining two days can be

(i) Sunday and Monday

(ii) Monday and Tuesday

(iii) Tuesday and Wednesday

(iv) Wednesday and Thursday

(v) Thursday and Friday

(vi) Friday and Saturday

(vii) Saturday and Sunday

For the leap year to contain 53 Sundays, last two days are either Sunday and Monday or Saturday and Sunday.

∴ Number of such favourable outcomes = 2

Total number of possible outcomes = 7

∴ P(a leap year contains 53 sundays) = 2/7

Q.- Three unbiased coins are tossed together. Find the probability of getting :

(i) All heads, (ii) Two heads

(iii) One head (iv) At least two heads.

Sol. Elementary events associated to random

experiment of tossing three coins are HHH, HHT, HTH, THH, HTT, THT, TTH, TTT

∴ Total number of elementary events = 8.

(i) The event "Getting all heads" is said to occur, if the elementary event HHH occurs i.e. HHH is an outcome. Therefore,

∴ Favourable number of elementary events = 1

Hence, required probability = 1/8

(ii) The event "Getting two heads" will occur, if one of the elementary events HHT, THH, HTH occurs.

∴ Favourable number of elementary events = 3

Hence, required probability = 3/8

(iii) The events of getting one head, when three coins are tossed together, occurs if one of the elementary events HTT, THT, TTH happens.

∴ Favourable number of elementary events = 3

Hence, required probability =3/8

(iv) If any of the elementary events HHH, HHT,HTH and THH is an outcome, then we say that the event "Getting at least two heads" occurs.

∴ Favourable number of elementary events = 4

Hence, required probability = 4/8 =1/2.

Q.- 17 Cards numbered 1, 2, 3 ... 17 are put in a box and mixed thoroughly. One person draws a card from the box. Find the probability that the number on the card is

(i) Odd

(ii) A prime

(iii) Divisible by 3

(iv) Divisible by 3 and 2 both.

Sol. Out of 17 cards, in the box, one card can be drawn in 17 ways.

∴ Total number of elementary events = 17.

(i) There 9 odd numbered cards, namely, 1, 3, 5, 7,9, 11, 13, 15, 17. Out of these 9 cards one card can be drawn in 9 ways.

∴ Favourable number of elementary events = 9.

Hence, required probability =9/17

(ii) There are 7 prime numbered cards, namely, 2, 3, 5, 7, 11, 13, 17. Out of these 7 cards one card can be chosen in 7 ways.

∴ Favourable number of elementary events = 7.

Hence, P (Getting a prime number) = 7/17

(iii) Let A denote the event of getting a card bearing a number divisible by 3. Clearly, event A occurs if we get a card bearing one of the numbers 3, 6, 9, 12, 15.

∴ Favourable number of elementary events = 5.

Hence, P (Getting a card bearing a number divisible by 3) = 5/17

(iv) If a number is divisible by both 3 and 2, then it is a multiple of 6. In cards bearing number 1, 2, 3 ..., 17 there are only 2 cards which bear a number divisible by 3 and 2 both i.e. by 6.

These cards bear numbers 6 and 12

∴ Favourable number of elementary events = 2

Hence, P (Getting a card bearing a number divisible by 3 and 2) = 2/17

Q.- A bag contains 5 red balls, 8 white balls, 4 green balls and 7 black balls. If one ball is drawn at random, find the probability that it is

(i) Black (ii) Red (iii) Not green.

Sol. Total number of balls in the bag

= 5 + 8 + 4 + 7 = 24

∴ Total number of elementary events = 24

(i) There are 7 black balls in the bag.

∴ Favourable number of elementary events = 7

Hence, P (Getting a black ball) =7/24

(ii) There are 5 red balls in the bag.

∴ Favourable number of elementary events = 5

Hence, P (Getting a red ball) = 5/24

(iii) There are 5 + 8 + 7 = 20 balls which are not green.

∴ Favourable number of elementary events = 20

Hence, P (No getting a green ball) =20/24 =5/6

Q.- (i) A lot of 20 bulbs contain 4 defective ones.

One bulb is drawn at random from the lot.What is the probability that this bulb is defective ?

(ii) Suppose the bulb drawn in (i) is not defective and is not replaced. Now one bulb is drawn at random from the rest. What is the probability that this bulb is not defective ?

Sol. (i) The total number of bulbs = 20

Total number of possible outcomes = 20

Number of favourable outcomes of defective bulbs = 4

P = Number of favourable outcomes/Total number of possible outcomes

(ii) The bulb drawn is not defective

Total number of bulbs without replacement = 19

Number of defective bulbs = 4

Number of non defective bulbs = 19 – 4 = 15

Number of favourable outcomes of non defective bulbs = 15

Total number of possible outcomes = 19

P = Number of favourable outcomes/Total number of possible outcomes

P (non defective) = 15/19

Q.- It is given that in a group of 3 students, the probability of 2 students not having the same birthday is 0.992. What is the probability that the 2 students have the same birthday ?

Sol. Probability of 2 students from a group of 3 students not having the same birthday = 0.992

Probability of 2 students from a group of 3 students having the same birthday

[∴ p + q = 1] = 1 – 0.992 = 0.008

Q.- A card is drawn at random from a well-shuffled pack of 52 cards. Find the probability that the card drawn is neither a red card nor a queen.

Sol. Number of red cards including 2 red

queens = 26

Number of black queens = 2

Therefore, number of red cards including 2 red

queens and 2 black queens = 26 + 2 = 28

Number of cards neither a red card nor a queen = 52 – 28 = 24

P = Number of favourable outcomes/Total number of possible outcomes

P (neither a red nor a queen card) =24/52=6/13

More question-

PROBABILITY

1. A card is drawn from a pack of cards numbered 1 to 52. The probability that the number on the card is a perfect square is
(a) 1/31
(b) 2/13
(c) 7/52
(d) 5/52

2. A die is thrown once, then the probability of getting a number greater than 3 is
(a) 1/2
(b) 2/3
(b) 6
(d) 0

3. When a die is thrown, the probability of getting an odd number less than 3 is
(a) 1/6
(b) 1/3
(c) 1/2
(d) 0

4. A card is drawn from a deck of 52 cards. The event ‘E’ is that card which is not ace of hearts. The number of outcomes favourable to E is
(a) 4
(b) 13
(c) 48
(d) 51

5. One ticket is drawn at random from a bag containing tickets numbered 1 to 40. The probability that the selected ticket has a number which is a multiple of 5 is
(a) 1/5
(b) 3/5
(c) 4/5
(d) 1/3

6. The probability of getting a bad egg in a lot of 400 is 0.035. The number of bad eggs in the lot is
(a) 7
(b) 14
(c) 21
(d) 28

7. The probability that a card drawn out of a packet of 52 is of diamond is
(a) 0
(b) 1/52
(c) 1/13
(d) 1/4

8. In simultaneous tossing of two coins, the probability of getting 2 tails is
(a) 0
(b) 1
(c) 1/2
(d) 1/4

9. Which of the following can not be the probability of an event ?
(a) 3/2
(b) 4%
(c) 0.9
(d) 3/7

10. An event is very unlikely to happen. Its probability is closest to
(a) 0.01
(b) 0.0001
(c) 0.1

11. The probability of sure event ‘is
(a) 0
(b) 1/2
(c) 1/4
(d) 1

12. If P(A) denotes the probability of an event A, then
(a) P(A) < 0
(b) P(A) > 1
(c) 0 ≤ P(A) ≤ 1
(d) −1 ≤ P(A) ≤ 1

13. If for any event E, P(E) = 0.3 then P(not E) is equal to
(a) 0.3
(b) −0.3
(c) 0.7
(d) −0.7

14. The probability expressed as a percentage of a particular occurrence can never be
(a) less than 100
(b) less than 0
(c) greater than 1
(d) number other than a whole number

15. The probability of getting two tails when three coins are tossed simultaneously is
(a) 1/8
(b) 1/2
(c) 3/8
(d) 5/8

16. A card accidently dropped from a pack of 52 cards. The probability of its being a card of diamond is
(a) 1/2
(b) 1/4
(c) 1/13
(d) 1/20

17. A letter of English alphabet is chosen at random. The probability that it is a letter of the word “MATHEMATICS” is
(a) 11/26
(b) 5/13
(c) 9/26
(d) 4/13

18. In a single throw of a pair of dice, the probability of getting the sum 12 is
(a) 5/36
(b) 1/9
(c) 1/18
(d) 1/36

19. In a single throw of a dice, the probability of getting a prime number is
(a) 2/3
(b) 1/6
(c) 1/3
(d) 1/2

20. Three coins are tossed. What is the probability of getting neither 3 heads nor 3 tails ?
(a) 1/2
(b) 1/3
(c) 2/3
(d) 3/4

21. The probability that a leap year should have exactly 52 Tuesday is
(a) 2/7
(b) 3/7
(c) 1
(d) 5/7

22. Among 52 cards, there are 12 face cards. Probability that a card drawn at random is not a face card is
(a) 3/13
(b) 9/13
(c) 10/13
(d) 3/4

23. If an event cannot occur, then its probability is
(a) 1
(b) 3/4
(c) 1/2
(d) 0

24. Which of the following cannot be the probability of an event ?
(a) 1/3
(b) 0.1
(c) 3%
(d) 17/16

25. An event is very unlikely to happen. Its probability is closes to
(a) 0.0001
(b) 0.001
(c) 0.01
(d) 0.1

26. The probability expressed as a percentage of a particular occurrence can never be
(a) Less than 100
(b) less than 0
(c) greater than 1
(d) anything but a whole number

27. A fair dice is rolled. The probability of getting a number more than six is
(a) 1 < 0
(b) ≥ 1
(c) 0
(d) Can not be determined

28. In tossing a fair die, the probability of getting an odd number or a number less than 4 is
(a) 2
(b) 1/2
(c) 2/3
(d) 3/4

29. The probability of getting 9 with two dice is
(a) 1/36
(b) 9/1
(c) 1/27
(d) 2/9

30. A card is drawn from well shuffled deck of playing cards. The probability of a face card is
(a) 1/13
(b) 3/13
(c) 4/13
(d) 2/13

31. In a single throw of a pair of dice, the probability of getting the sum a perfect square is
(a) 1/18
(b) 7/36
(c) 1/6
(d) 2/9

32. If P(E) = 0.05 the P(not E) i.e. P(E) = _______ ?
(a) 0.05
(b) 0.5
(c) 0.9
(d) 0.95

Short Questions

1. Box A contains 25 slips of which 19 are marked Rs.1 and other are marked Rs.5 each. Box B contains 50 slips of which 45 are marked Rs.1 each and others are marked Rs.13 each. Slips of both the boxes are poured into a third box and reshuffled. A slip is drawn at random. What is the probability that it is marked other than Rs.1 ?

2. A child’s game has 8 triangles of which 3 are blue and rest are red, and 10 squares of which 6 are blue and rest are red. One piece is lost at random. Find the probability that it is a : (i) triangle (ii) square (iii) square of blue colour (iv) triangle of red colour.

3. A carton of 24 blubs contain 6 defective bulbs. One bulb is drawn at random. What is the probability that the bulb is not defective ? If the bulb selected is defective and it is not replaced and a second bulb is selected at random from the rest, what is the probability that the second bulb is defective ?

4. A lot consists of 48 mobile phones of which 42 are good, 3 have only minor defects and 3 have major defect Varnika will buy a phone if it is good but the trader will only buy a mobile if it has no major defect. One phone is selected at random from the lot. What is the probability that it is (i) acceptable to varnika ? (ii) acceptable to the trader ?

5. In a game, the entry fee is Rs.5. The game consists of tossing a coin 3 times. If one or two heads show, Sweta gets her entry fee back. If she shows 3 heads, the receives double the entry fees. Otherwise, she will lose. After tossing a coin three times, find the probabilities that she (i) loses the entry fee (ii) gets double entry fee (iii) just gets her entry fee

6. A lot of 60 bulbs contain 12 defective ones. One bulbs drawn at random from the lot. What is the probability that this bulb is defective ? Suppose the bulb draw in first attempt is defective and is not replaced. Now, one bulb is drawn at random from the rest. What is the probability that this bulb is not defective ?

7. A bag contains 5 black, 7 red & 3 white balls. A ball is drawn from the bag at random. Find the probability that the ball drawn is (i) red (ii) black or white (iii) not black.

8. Find the probability of getting 53 Fridays (i) in a leap year (ii) in a non-leap year.

9. Out of 400 bulbs in a box. 15 bulbs are defective. One bulb is taken out at random from the box. Find the probability that the drawn bulb is not defective.

10. A card is drawn at random from a pack of 52 playing cards. Find the probability that the card drawn is neither an ace nor a jack.

11. The king, queen and jack of diamond are removed from a deck of 52 playing cards and then well shuffled. Now, one card is drawn at random from the remaining cards. Determine the probability that the card is (i) a jack (ii) a heart (iii) a red queen

12. Cards bearing numbers 1, 3, 5 ….. 35 are kept in a bag. A card is drawn at random from the bag. Find the probability of getting a card bearing (i) a prime no. less than 15 (ii) a no. divisible by 3 and 5.

13. An integer is chosen between 0 and 100. What is the probability that it is (i) divisible by 9 ? (ii) not divisible by 9 ?

14. A bag contains cards which are numbered from 2 to 90. A card is drawn at random from the bag. Find the probability that it bears (i) a two digit number (ii) a number which is a perfect square.

15. A card is drawn at random from a pack of 52 playing cards. Find the probability that the card drawn is neither a black card not a king.

16. Two dice are thrown together and the product of numbers appearing on them is noted. Find the probability that the product is less than 12.

17. A die is thrown twice. What is the probability that (i) 3 will not come up either time ? (ii) 3 will come up atleast once ?

18. A die has its six faces marked 0, 1, 1,1, 6, 6. Two such dices are thrown together and the total score is recorded. (i) How many different scores are possible ? (ii) What is the probability of getting a total of 7 ?

19. A bag contains white, black and red balls only. A ball is drawn at random from the bag. The probability of getting a white ball is 3/10 and that of a black ball is 2/5. Find the probability of getting a red ball if the bag contains 20 black balls, then find the total no. of balls in the bag.

20. A bag contains 7 green, 10 blue and 5 red balls. A ball is drawn at random. Find the probability of this ball being a (i) blue ball (ii) red ball or green ball (iii) not a green ball.

21. A bag contains 24 balls of which x are red, 2x are white and 3x are blue. A ball is selected at random. What is the probability that the drawn ball is (i) not white ? (ii) blue ?

LONG TYPES QUESTIONS

1. A bag contains 6 red, 5 black and 4 white balls. A ball is drawn from the bag at random. Find the probability that the ball drawn is (i) white (ii) red (iii) not black (iv) red or white.

2. 18 cards, numbered 1, 2, 3, …… 18 are put in a box and mixed thoroughly. A card is drawn at random from the box. Find the probability that the card drawn bears (i) an even numbers (ii) a number divisible by 2 or 3.

3. A card is drawn at random from a well shuffled deck of playing cards. Find the probability that the card drawn is (i) a card of spade or an ace (ii) a red king (iii) neither a king nor a queen (iv) either a king or a queen.

4. Cards marked with numbers 3, 4, 5……….. 50 are placed in a box and mixed thoroughly one card is drawn at random from the box. Find the probability that number on the drawn card is (i) divisible by 7 (ii) a number which is a perfect square ?

5. The probability of gussing the correct answer to a certain test is P/12. If the probability of not guessing the correct answer to this question is 1/3. Find the value of ‘P’.

6. A number is selected at random from the number 3, 5, 5, 7, 7, 7, 9, 9, 9, 9. Find the probability that the selected number is their average.

7. If a number x is chosen from the number 1, 2, 3 and a number y is selected from the numbers 1, 4, 9. Find the probability that xy = 10.

8. A number ‘x’ is chosen from the numbers −4, −3, −2, −1, 0, 1, 2, 3, 4. Find the probability that |x| < 3.

9. A die has six faces marked 0, 1, 1, 1, 6, 6. Two such dice are thrown together and the total is recorded. (i) How many different scores are possible ? (ii) What is the probability of getting a total of 7 ?

10. A bag contains 5 red balls & some blue balls. If the probability of drawing a blue ball is double that of a red ball, find the number of blue balls in the bag.

Value Based Questions

1. In a survey, it was found that 40% people use petrol, 35% use diesel and remaining use CNG for their vehicles. Find the probability that a person chosen at random use CNG.
a) Which fuel out of the above three is appropriate for the welfare of the society?

2. In a survey, it was found that 30% of the population is using non – biodegradable products. While the remaing is using biodegradableproducts.What is the probability that a person chosen at random uses non – biodegradable products?
i) Which type of products should be used in a society for its proper development – biodegradable or non – biodegradable? Justify your answer.

3. A school gives awards to the students of each class – 5 for bravery, 3 for punctuality, 3 for full attendance, 4 for social service and 5 for self confidence. An awarded student is selected at random. What is the probability that he is being awarded for (i) punctuality (ii) Self Confidence.
a) Which value out of the above five is most important for the development of society? Justify your answer.

4. Arushi, mahi and Saina were fighting to get first chance in a game. Arushi says, “Let us toss two coins. If both head appear, Mahi will take first chance, if both tail appear, Saina will get it and if one head and one tail appears, I will get the chance.”
i) What is the probability of Arushi getting the 1st chance?
ii) Is her decision fair?
iii) What quality of her character is being depicted here?

5. In a town, 75% population uses biodegradable material and the remaining uses non – biodegradable material. A person is chosen at random from the town.
i) What is the probability that he uses non – biodegradable material?
ii) Which type of material should we use and why?

6. A survey was conducted in a residential society in which it was discovered that 45 households believe in hard work, 28 believe in self confidence and 12 believe in punctuality for attaining success in life. What is the probability that a person chosen at random believes in self confidence?
Which value, according to you, contributes the most in attaining success in life?

7. Ina food survey, 80% of the food samples were found to be adulterated while the remaining samples were pure. If the sample is selected at random, what is the probability that the food is adulterated?
i) What does the result of the survey show?
ii) How does food adulteration affect our health?

8. In a self assessment survey, 45% claimed that they are patriotic, 42% claimed to be non – violent and the remaining claimed to be optimistic. What is the probability of a person chosen at random to be claiming himself (A) patriotic (b) optimistic?
Which value do you claim for yourself out of the given three and why?

9. In a society, certain number of people worked for three campaigns. Some worked for “ Say no to plastic”. Some for “Say no to crackers” and the remaining for “Say no to child labour”. A person is selected at random from the society. The probability of getting a person from first campaign is 3/10 and that of 2nd campaign is 2/5. Find the probability of getting a person who worked for the third campaign. If the number of persons in 2nd campaign was 20, find the total number of persons involved in the three campaigns. Are such campaigns helpful in spreading awareness among the people? Give your views.

Question. A card is drawn from a well-shuffled deck of playing cards. Find the probability of drawing
(i) a face card (ii) a red face card.

Answer : Random drawing of cards ensures equally likely outcomes

(i) Number of face cards (King, queen and Jack of each suits) = 3 × 4 = 12

Total number of cards in a deck = 52

∴ Total number of possible outcomes = 52

P = Number of favourable outcomes/Total number of possible outcomes

P (drawing a face card) = 12/52=3/13

(ii) Number of red face cards 2 × 3 = 6

Number of favourable outcomes of drawing red face card = 6

P = Number of favourable outcomes/Total number of possible outcomes

P (drawing of red face card) = 6/52=3/26

Question. A box contains 12 balls out of which x are black.

(i) If one ball is drawn at random from the box, what is the probability that it will be a black ball ?

(ii) If 6 more white balls are put in the bag, the probability of drawing a black ball will double than that in (i). Find x.

Answer : Random drawing of balls ensures equally likely

outcomes

Total number of balls = 12

∴ Total number of possible outcomes = 12

Number of black balls = x

(i) Out of total 12 outcomes, favourable outcomes = x

P (black ball) = Number of favourable outcomes/Total number of possible outcomes = x/12

(ii) If 6 more black balls are put in the bag, then

Total number of black balls = x + 6

Total number of balls in the bag = 12 + 6 = 18

P (black ball) = Total number of possible outcomes/Number of favourable outcomes = x + 6/12 + 6

According to the question,

Probability of drawing black ball in second case

= 2 × Probability drawing of black ball in first case

=> x + 6/18 =2 (x/12)

x + 6/18 =x/6

=> 6x + 36 = 18 x

=> 12x = 36

=> x = 3

Hence, number of black balls = 3

Question. A box contains 20 balls bearing numbers, 1, 2, 3, 4, ... 20. A ball is drawn at random from the box. What is the probability that the number on the balls is

(i) An odd number

(ii) Divisible by 2 or 3

(iii) Prime number

(iv) Not divisible by 10

Answer : Total number of possible outcomes = 20

Probability = Number of favourable outcomes/Total number of possible outcomes

(i) Number of odds out of first 20 numbers = 10

Favourable outcomes by odd = 10

P(odds) = Favourable outcomes of odd/Total number of possible outcomes

= 10/20=1/2

(ii) The numbers divisible by 2 or 3 are 2, 3, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20.

Favourable outcomes of numbers divisible by

2 or 3 = 13

P (numbers divisible by 2 or 3)

= Favourable outcomes of divisible by 2 or 3/Total number of possible outcomes =13/20

(iii) Prime numbers out of first 20 numbers are 2, 3, 5, 7, 11, 13, 17, 19

Favourable outcomes of primes = 8

P(primes)

= Favourable outcomes of primes/Total number of possible outcomes

= 8/20=2/5

(iv) Numbers not divisible by 10 are 1, 2, ... 9, 11, ...19

Favourable outcomes of not divisible by 10

= 18

P(not divisible by 10) = Favourable outcomes of not divisible by 10/Total number of possible outcomes

= 18/20=9/10

Very Short Answer Type Questions

Question. A card is drawn from a pack of 52 cards. What is the probability of getting an ace ?

Answer : 1/13

Question. When a card is drawn from a pack of 52 cards.Find the probability that it may be either a king or a queen.

Answer : 2/13

Question. One card is drawn from a pack of 52 cards.Find the probability that the card drawn is red or king.

Answer : 7/13

Short Answer Type Questions

Question. The king, queen and jack of clubs are removed from a deck of 52 playing cards and then well shuffled. One card is selected from the remaining cards. Find the probability of getting

(i) a heart (ii) a king

(iii) a club (iv) the ‘10’ of hearts

Answer : (i) 13/49 (ii)3/49 (iii) 10/49 (iv) 1/49

Question. If a coin is tossed two times, what is the probability of getting ‘head’ at least once ?

Answer : 3/4

Question. A number is chosen at random among the first 100 natural numbers. Find the probability that the number chosen being a multiple of 5.

Answer : 1/5

Question. From a set of 17 cards, numbered 1, 2, ..., 17,one is drawn. What is the probability that is number is multiple of 3 or 7 ?

Answer : 7/17

More question-

Question. Two dice are thrown together. Find the probability that the product of the numbers on the top of the dice is a) 6 b) 12 c) 7
Answer : (1/9, 1/9, 0)

Question. Two different dice are thrown at the same time. Find the probability that the sum of the two numbers appearing On the top of the dice is 7
Answer : (1/6)

Question. A pair of dice is tossed once, find the probability of getting
a) a total of 2
b) a total of 5
c) an even number as the sum
d) same number on each dice
Answer : (1/36)
(1/9)
(1/2)
(1/6)

Question. A die is thrown once. Find the probability of getting the following:
a) a prime number
b) a number lying between 2 and 5
Answer : (1/2)
(1/3)

Question. A card is drawn at random from a well shuffled pack of playing cards. Find the probability of getting a red face card
Answer : (3/26)

Question. A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball from the bag is thrice that of red ball, find the number of blue balls in the bag
Answer : (15)

Question. A bag contains 6 red, 3 black and 6white balls. A ball is selected at random from the bag. Find the probability that the selected ball is
a) Red or black b) not black
Answer : (3/5, 4/5)

Question. Cards numbered 2,3, 4, 5, 6, -------,49 are put in a box and mixed thoroughly. If one card is drawn at random Find the probability that the number on the card is
a) Even number
b) rime number
c) Divisible by 6
d) A perfect square
Answer : (1/2)
(5/16)
(1/6)
(1/8)