CBSE Class 10 Maths Probabilty Worksheet

VERY SHORT ANSWER TYPE QUESTIONS :

Question. From a well-shuffled pack of cards, a card is drawn at random. Find the probability of getting a black queen. 
Answer : ∵ Total number of cards = 52
Since, the number of black queens = 2
∴ Number of favourable outcomes = 2
⇒ P(E) = 2/52 = 1/26.

Question. Cards bearing numbers 3 to 20 are placed in a bag and mixed thoroughly. A card is taken out from the bag at random. What is the probability that the number on the card taken out is an even number? 
Answer : Total number of cards (3 to 20) = 18
∴ Number of possible outcomes = 18
Since cards having even numbers (4, 6, 8, 10, 12, 14, 16, 18 and 20) are 9,
∴ Number of favourable outcomes = 9
∴ P(E) = 9/18 or 1/2.

Question. Cards each marked with one of the numbers 6, 7, 8, ....., 15 and placed in a box and mixed thoroughly. One card is drawn at random from the box. What is the probability of getting a card with number less than 10? 
Answer : ∵ There are 10 cards.
∴ Total number of possible outcomes = 10
Cards marked with a number less than 10 are: 6, 7, 8 and 9
i.e. The number of favourable outcomes = 4
∴ P(E) = 4/10 or 2/5.

Question. A bag contains 4 red and 6 black balls. A ball is taken out of the bag at random. Find the probability of getting a black ball. 
Answer : Total number of balls = 4 + 6 = 10
⇒ All possible outcomes = 10
Since, number of black balls = 6
∴ Number of favourable outcomes = 6
⇒ P(E) = 6/10 or 3/5 .

Question. Find the probability that a number selected from the numbers 1 to 25 which is not a prime number when each of the given number is equally likely to be selected.
Answer : Total number of given numbers = 25
Since the numbers 2, 3, 5, 7, 11, 13, 17, 19 and 23 are prime number.
There are 9 numbers.
∴ Number of numbers that are not prime = 25 − 9 = 16
∴ Number of favourable outcomes = 16
⇒ Required probability = 16/25.

Question. What is the probability that two different friends have different birthdays? (Ignoring leap year).
Answer : Number of days in a year = 365
⇒ Number of possible outcomes = 365
Since they have different birthdays.
∴ Number of favourable outcomes = 365 − 1 = 364
∴ P(E) = 364/365.

Question. A letter is chosen at random from English alphabet. Find the probability that the letter chosen precedes ‘g’.
Answer : Total number of letters in English alphabet is 26.
∴ Total number of possible outcomes = 26
∵ Letters preceding ‘g’ are:
a, b, c, d, e and f
∴ Favourable outcomes = 6
⇒ Required probability = 6/26 = 3/13.

Question. A die is thrown once. Find the probability of getting an odd number.
Answer : Total number of possible outcomes = 6                                                                                            [∵ Numbers 1 to 6 are marked on the faces of a die]
∵ odd numbers are 1, 3 and 5
∴ Favourable outcomes = 3
∴ Required probability = 3/6 = 1/2.

Question. A box contains cards marked with numbers 5 to 20. A card is drawn from the bag at random. Find the probability of getting a number which is a perfact square. 
Answer : ∵ Total number of cards = 16
∴ Possible outcomes are 16.
Since the numbers 9 and 16 are perfect numbers,
⇒ Number of favourable outcomes = 2
∴ P (E) = 2/16 or 1/8.

Question. A bag contains 9 black and 12 white balls. One ball is drawn at random. What is the probability that the ball drawn is black?
Answer : Total number of balls = 9 + 12 = 21
⇒ Number of possible outcomes = 21
Number of black balls = 9
⇒ Number of favourable outcomes = 9
∴ Required probability = 9/21 = 3/7.

Question. A die is thrown once. Find the probability of getting a number less than 3.
Answer : Numbers on the faces are 1, 2, 3, 4, 5 and 6.
∴ Number of possible outcomes = 6
Numbers less than 3 are 1 and 2.
⇒ Number of favourable outcomes = 2
∴ P(E) = 2/6 or 1/3.

Question. A card is drawn at random from a well-shuffled deck of 52 cards. What is the probability of getting a black king? 
Answer : ∵ Total number of cards = 52
∴ Number of possible outcomes = 52
Number of black king = 2
∴ P(Black king) = 2/52 = 1/26.

Question. A die is thrown once. Find the probability of getting a number greater than 5. 
Answer : Total number of possible outcomes = 6
Since only one number i.e., 6 is greater than 5
∴ Favourable number of outcomes = 1
⇒ P(E) = 1/6.

Question. A box contains 3 blue, 2 white and 4 red marbles. If a marble is drawn at random from the box, what is the probability that it will not be a white marble?
Answer : Total number of balls = 3 + 2 + 4 = 9
∴ Number of possible outcomes = 9
Since, number of white balls = 2
∴ Number of balls which are not white
= 9 − 2 = 7
⇒ Number of favourable outcomes = 7
∴ P(E) = 7/9.

Question. Two friends were born in the year 2000. What is the probability that they have the same birthday ?
Answer : Since the year 2000 was a leap year,
∴ Total number of days in the year = 366
∵ They have the same birthday.
∴ Number of favourable outcomes = 1
⇒ P(E) = 1/366.

Question. A letter of English alphabet is chosen at random. Determine the probability that the letter is a consonant. 
Answer : There are 26 letters in English alphabets.
⇒ Possible outcomes = 26
Q There are 5 vowels (a, e, i, o, u) and remaining are consonants.
∴ Number of consonants = 26 – 5 = 21
⇒ Favourable outcomes = 21
∴ P(consonants) = 21/26

Question. Find the probability of obtaining 7 on a single toss of one die.
Answer : Numbers marked on a die are:
1 , 2 , 3 , 4 , 5 , 6
∴ There are six different possible outcomes.
But none of these outcomes would produce a 7.
⇒ Favouable outcome = 0
∴ P₍₇₎ = 0/6 = 0
When an event cannot possibly succeed, we say it is an impossible event and probability of an impossible event is zero.
i.e. P_{(impossible event)} = 0

SHORT ANSWER TYPE QUESTIONS :

Question. Two dice are thrown at the same time and the product of numbers appearing on them is noted.
Find the probability that the product is less than 9.
Answer : Total number of possible outcomes = 6 × 6 = 36
∵ The outcomes such that the product of numbers appearing on the faces is less than 9 are:
(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (3, 1), (3, 2), (4, 1),
(4, 2), (5, 1) and (6, 1). 
∴ Number of favourable outcomes = 16
⇒ Required probability = 16/36 = 4/9.

Question. The king, queen and jack of diamonds are removed from a pack of 52 cards are then the pack is well-shuffled. A card is drawn from the remaining cards. Find the probability of getting a card of
(i) diamonds
(ii) a Jack 
Answer : ∵ There are 52 card in the pack.
And number of cards removed = 3                                            [1 king + 1 queen + 1 jack = 3 cards]
∴ Remaining cards = 52 − 3 = 49
∴ (i) P_{(a diamond)} = 13 − 3/49 = 10/49                                       [∵ Total diamonds are 13]
(ii) P(a jack) = 4 − 1/49 = 3/49                                                 [∵ Total jacks are 4]

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 : Numbers from 5 to 50 are 46.
∴ Total number of possible outcomes = 46.
(i) Prime numbers (less than 10) are 5, 7.
∴ Favourable outcomes = 2
⇒ P_{(prime number less than 10)} = 2/46 = 1/23
(ii) Perfect square are 9, 16, 25, 36 and 49
∴ Number of favourable outcomes = 5
⇒ P_{(perfect square)} = 5/46.

Question. An integer is chosen between 0 and 100. What is the probability that it is divisible by 7?
Answer : ∵ Numbers between 0 and 100 are 99.
∴ Total possible outcomes = 99
Since following numbers are divisible by 7 :
7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91 and 98.
∴ Favourable outcomes = 14
⇒ Required probability = 14/99.

Question. In a game of chance there is spinning of an arrow which comes to rest pointing at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8 and there are equally likely outcomes. What is the probability that it will point at
(i) 7?
(ii) an odd number?
(iii) a number less than 9? 
Answer : Since, following numbers are marked on the disc:
    1, 2, 3, 4, 5, 6, 7, 8

(iii) Q The numbers less than 9 on the disc are:
1, 2, 3, 4, 5, 6, 7, 8, (i.e. 8 outcomes)
∴ Favourable outcomes = 8
⇒ P_{(number less than 9)} = 8/8 = 8

Question. Find the probability that a number selected at random from numbers 3, 4, 5, ....., 25 is prime.
Answer : Total numbers are 23.
∴ Number of possible outcomes = 23
Since, prime numbers are 3, 5, 7, 11, 13, 17, 19 and 23.
∴ Number of favourable outcomes = 8
⇒ P (E) = 8/23.

Question. A die is thrown once. Find the probability of getting:
(i) an even prime number.
(ii) a multiple of 3. 
Answer : Total numbers on the faces of a die are 1, 2, 3, 4, 5 and 6
⇒ Number of favourable outcomes = 6
(i) Even prime number is only one i.e. 2
∴ Favourable outcome = 1
⇒ P_{(even prime number)} = 1/6
(ii) Multiples of 3 are 3 and 6
∴ Favourable outcomes are 2.
⇒ P_{(multiple of 3)} = 2/6 = 1/3.

Question. From a group of 2 boys and 3 girls, two children are selected at random. Find the probability such that at least one boy is selected.
Answer : Let B₁ and B₂ be two boys and G₁, G₂ and G₃ be the three girls
Since two children are selected at random,
∴ Following are the possible groups:
B₁B₂, B₁G₁, B₁G₂, B₁G₃, B₂G₁, B₂G₂, B₂G₃, G₁G₂, G₁G₃, G₂G₃
∴ Total number of possible outcomes = 10
Since, one boy is to be selected,
∴ Favourable outcomes are:
B₁B₂, B₁G₁, B₁G₂, B₁G₃, B₂G₁, B₂G₂ and B₂G₃.
⇒ Number of favourable outcomes = 7
∴ Required probability = 7/10.

Question. A bag contains 4 red, 5 black and 3 yellow balls. A ball is taken out of the bag at random. Find that the ball taken out is of:
(i) yellow colour
(ii) not of red colour. 
Answer : Total number of balls = 4 + 5 + 3 = 12
⇒ Total number of possible outcomes = 12
(i) ∵ Number of yellow balls = 3
∴ Number of favourable outcomes = 3
⇒ P_(yellow) = 3/12 = 1/4
(ii) Number of balls that are not red = 12 − 4 = 8                             [∵ There are 4 red balls]
∴ Favourable outcomes = 8
⇒ P_{(not red)} = 8/12 = 2/3.

Question. A bag contains 7 red, 5 white and 3 black balls. A ball is drawn at random from the bag. Find the probability that the drawn ball is neither white nor black.
Answer : Total number of balls
= 7 + 5 + 3
= 15
∵ Number of white balls = 5
Number of black balls = 3
∴ Number of balls that are neither white nor black = 15 − [5 + 3]
= 15 − 8
= 7
∴ Required probability = 7/15.

Question. Cards with numbers 2 to 101 are placed in a box. A card is selected at random. Find the probability that the card has a square number. 
Answer : Number of numbers between 2 to 101 are 100
∴ Total number of possible outcomes = 100
Since, the perfect numbers between 2 and 101 are:
4, 9, 16, 25, 36, 49, 64, 81 and 100
∴ Number of favourable outcomes = 9
⇒ Required probability = 9/100.

Question. A bag contains 10 red, 5 blue and 7 green balls. A ball is drawn at random. Find the probability of this ball being not a blue ball.
Answer : Total number of balls = 10 + 5 + 7 = 22
∴ Number of possible outcomes = 22
Since there are 5 blue balls.
∴ Number of balls which are not blue
= 22 − 5 = 17
∴ Favourable outcomes = 17
⇒ Required probability = 17/22.

Question. A box contains 20 cards, numbered from 1 to 20. A card is drawn from the box at random. Find the probability that the number on the drawn card is:
(i) even
(ii) multiple of 3.
Answer : Total numbers from 1 to 20 are 20
∴ Number of possible events = 20
(i) Even numbers are:
2, 4, 6, 8, 10, 12, 14, 16, 18 and 20
∴ Number of favourable outcomes = 10
⇒ Probability of getting an even number = 10/20 = 1/2
(ii) Since, multiples of 3 are:
3, 6, 9, 12, 15 and 18
∴ Number of favourable outcomes = 6
⇒ Probability of getting a multiple of 3
= 6/20 = 3/10.

Question. Two dice are thrown simultaneously. What is the probability that
(i) 5 will not come up on either of them?
(ii) 5 will come up on at least one?
(iii) 5 will come up at both dice?
Answer : ∵ The two dice are thrown simultaneously
∴ Possible outcomes are = 6 × 6 = 36
(i) When 5 will not come up on either of them:
Favourable outcomes are: 36 − 11 = 25
∴ P_{(5 will not come up on either dice)} = 25/36
(ii) When 5 will come on at least one dice:
Favourable outcomes are: 36 − 25 = 11
∴ P_{(5 will come on at least one dice)} = 11/36
(iii) When 5 will come up on either dice:
Favourable outcome is only one i.e. (5, 5)
∴ P_{(5 on both dice)} = 1/36.

Question. A card is drawn at random from a well-shuffled deck of playing cards. Find the probability of drawing a
(i) face card
(ii) card which is neither a king nor a red card. 
Answer : Total number of cards = 52
(i) Total number of face cards = 12                                 [4 Jacks + 4 Queens + 4 Kings]
∴ Number of favourable outcomes = 12
⇒ P_(face) = 12/52 = 3/13
(ii) Number of kings = 4
Number of red cards = 13 + 13 = 26
∴ Number of cards that are neither a red nor a king = 52 − 4 − 26 + 2 (red kings)
= 24
⇒ Favourable outcomes = 24
∴ P_{(neither king nor red)} = 24/52 = 6/13

Question. Two 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 more than 9. 
Answer : Following are the possible outcomes for two dice thrown simultaneously:
(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)
∴ Total number of possible outcomes = 36
Following outcomes have a sum of more than 9:
(4, 6), (6, 4), (5, 5), (5, 6), (6, 5) and (6, 6)
i.e. Favourable outcomes = 6
∴ The required probability = 6/36 or 1/6.

Question. In a bag-X, there are four cards numbered 1, 3, 5 and 7 respectively. In an another bag-Y, there are three cards numbered 2, 4 and 6 respectively. A card is drawn at random from each bag.
(a) Write all the possible outcomes.
(b) Find the probability that the sum of these two cards drawn is:
(i) 7
(ii) even
(iii) more than 7
Answer : (a) There are 12 possible outcomes

Question. A die is thrown once. Find the probability of getting:
(i) a prime number
(ii) a number divisible by 2. 
Answer : ∵ The numbers on the faces of a die are 1, 2, 3, 4, 5 and 6.
∴ Number of possible outcomes = 6
(i) Prime numbers are 2, 3 and 5
∴ Number of prime numbers = 3
⇒ Number of favourable outcomes = 3
∴ P_{(prime number)} = 3/6 = 1/2
(ii) Numbers divisible by 2 are 2, 4 and 6
∴ Favourable outcomes are 3.
⇒ P_{(divisible by 2)} = 3/6 = 1/2.

Question. A bag contains tickets, numbered 11, 12, 13, ....., 30. A ticket is taken out from the bag at random.
Find the probability that the number on the drawn ticket
(i) is a multiple of 7
(ii) is greater than 15 and a multiple of 5. 
Answer : Total number of tickets = 20                                          [∵ Numbers from 11 to 30 are 20]
(i) ∵ Multiples of 7 are 14, 21 and 28
∴ Number of favourable outcomes = 3
⇒ P_{(a multiple of 7)} = 3/20
(ii) ∵ The numbers that are greater than 15 and multiples of 5 are: 20, 25 and 30
∴ Number of favourable outcomes = 3
⇒ P_{(multiples of 5 and greater than 15)} = 3/20.

Question. Two dice are thrown at the same time. Find the probability of getting different numbers on thedice. 
Answer : Since the two dice are thrown simultaneously.
∴ Total number of outcomes = 6 × 6 = 36
Number of outcomes for getting same numbers on both dice = 6
⇒ P (same numbers) = 6/36 = 1/6
Now, P (different numbers) + P (same numbers) = 1
⇒ P (different numbers) = 1 − P (same numbers)
= 1 −1/6
= 5/6.

Question. Two different dice are rolled simultaneously. Find the probability that the sum of numbers appearing on the two dice is 10. 
Answer : When two different dice are rolled then possible outcomes are :
(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)
∴ Number of total outcomes = 36
∵ Sum of (5, 5), (6, 4) and (4, 6) is 10.
∴ No of favourable outcomes = 3
⇒ Required Probability = 3/36 or 1/12

Question. A bag contains 5 red, 4 blue and 3 green balls. A ball is taken out of the bag at random. Find the probability that the selected ball is
(i) of red colour
(ii) not of green colour. 
Answer : Total number of balls = 5 + 4 + 3 = 12
⇒ Number of possible outcomes = 12
(i) ∵ Number of red balls = 5
∴ Favourable outcomes = 5
⇒ P_{(red ball)} = 5/12
(ii) ∵ Number of green balls = 3
∴ Number of ball which are not green = 12 − 3 = 9
⇒ Favourable outcomes = 9
∴ P_{(not green)} = 9/12 = 3/4.

Question. A coin is tossed two times. Find the probability of getting at most one head.
Answer : Since, the coin is thrown two times.
∴ Possible out comes = 4
Favourable outcomes are TT, TH, HT
i.e., Number of favourable outcomes = 3
∴ P_{(atmost one head)} = 3/4.

Question. Two dice are thrown at the same time. Find the probability of getting same number on both dice.
Answer : Total number of outcomes = 6 × 6 = 36
∴ Following are the outcomes that have same number on both dice are:
(1, 1), (2, 2), (3, 3), (4, 4), (5, 5) and (6, 6)
∴ Favourable outcomes = 6
⇒ Required probability = 6/36 = 1/6.

Question. A letter of English alphabet is chosen at random. Determine the probability that the letter is consonant.
Answer : ∵ There are 26 letters of English alphabet
∴ Number of possible outcomes = 26
Since, there are 21 consonants of the English alphabets.
∴ Favourable outcomes = 21
⇒ Required probability = 21/26.

Question. There are 40 students in class X of whom 25 are girls and 15 are boys. The class teacher has to select one student as a class representative. She writes the name of each student on a separate card.
The cards being identical and she puts cards in a bag and stirs throughly. She then draws one card from the bag. What is the probability that the name written on the card is the name of a:
(i) girl
(ii) a boy
Answer : Total number of students = 40
⇒ Number of possible outcomes = 40
(i) Q There are 25 girls in the class
∴ Number of favourable outcomes = 25
⇒ P(name of a girl) = 25/40 5/8
(ii) Q Number of boys = 15
∴ Number of favourable outcomes = 15
⇒ P(name of a boy) = 15/40 3/8

Please click on below link to download CBSE Class 10 Maths Probabilty Worksheet