CBSE Class 9 Mathematics Probability Set A

1 In an experiment, what is the sum of probabilities of all events?
(A) 0.5
(B) 1
(C) - 2
(D) 3/8
Answer : B

2 In a throw of a die, what is the probability of getting a prime number?
(A) 2
(B) 1/2
(C) 3/2
(D) 6
Answer : B

3 Find the probability that a vowel selected at random in the English alphabet is an "i".
(A) 1/5
(B) 1/26
(C) 1/6
(D) 4/5
Answer : A

4 Determine the probability of three coins falling all heads up when tossed simultaneously.
(A) 1/2
(B) 1/6
(C) 1/8
(D) 7/8
Answer : C

5 The probability of happening of an event is 45%. Find t he probability of that event.
(A) 45
(B) 4.5
(C) 0.45
(D) 0.045
Answer : C

6 When two dice are thrown, what is the probability of getting a number always greater than 4 on the second dice?
(A) 1/6
(B) 1/3
(C) 1/36
(D) 2/3
Answer : B

7 Determine the probability of getting an even number when a die is rolled.
(A) 1/6
(B) 1/36
(C) 1/2
(D) 1/3
Answer : C

8 Two numbers are chosen from 1 to 5. Find the probability for the two numbers to be consecut ive.
(A) 1/5
(B) 2/5
(C) 1/10
(D) 3/5
Answer : B

9 One card is drawn from a well-shuffled deck of 52 cards. Find the probability of drawing a '1 0' of a black suit.
(A) 1/13
(B) 1/26
(C) 5/13
(D) 1/52
Answer : B

10 Two dice are thrown at a time. What is the probability that the difference of the numbers shown on the dice is 1?
(A) 5/18
(B) 1/36
(C) 1/6
(D) 7/36
Answer : A

11 A bag contains 3 white and 5 red balls. If a ball is drawn at random, find the probability that it is red.
(A) 3/8
(B) 5/8
(C) 3/15
(D) 5/15
Answer : B

12 From a normal pack of cards, a card is drawn at random. What is t he probability of getting a jack or a king?
(A) 1/26
(B) 1/52
(C) 2/13
(D) 1/13
Answer : C

13 A card is drawn from a packet of 100 cards numbered 1 t o 1 00. Find the probability of drawing a number which is a square.
(A) 1/10
(B) 100
(C) 100
(D) 50
Answer : A

14 Find the probability for a randomly selected number out of 1, 2, 3, 4, ..... , 25 to be a prime number.
(A) 7/25
(B) 23/25
(C) 2/5
(D) 9/25
Answer : D

15 A bag contains 5 red balls and 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 t he bag.
(A) 15
(B) 12
(C) 5
(D) 10
Answer : D

16 A book containing 100 pages is opened at random. Find the probability that a doublet page is found.
(A) 9/100
(B) 9/10
(C) 1/10
(D) 1/5
Answer : A

17 If a coin is tossed twice, what is the probability of getting at least one head?
(A) 1/2
(B) 1/4
(C) 3/4
(D) 2/3
Answer : C

18 What is the probability of getting a number great er than 2 or an even number in a single throw of a fair die?
(A) 1/3
(B) 2/3
(C) 5/6
(D) 1/6
Answer : C

19 Find the probability that in a family of 3 children, there will be at least one boy.
(A) 3/4
(B) 1/8
(C) 3/8
(D) 5/8
Answer : A

20 What is the probability that a non-leap year cont ains 53 Saturdays?
(A) 2/7
(B) 1/7
(C) 2/365
(D) 1/365
Answer : B

21 A bag contains 12 balls out of which x are white. If one ball is drawn at random, what is the probability that it will be a white ball?
(A) x
(B) x/2
(C) x/12
(D) 12x
Answer : C

22 A coin is t ossed 150 t imes and data about the outcomes is given in the table

Outcomes	H	T
Frequency	90	60

What is the probabilit y of getting a head in a trial?
(A) 1/2
(B) 1/3
(C) 3/5
(D) 2/5
Answer : C

(23 - 24): Two coins are tossed simultaneously 80 times and data is recorded in the table given.

Number of heads in a trial	0	1	2
Frequency	20	35	25

23 What is the probability of get ting two heads?
(A) 1/4
(B) 1/2
(C) 7/16
(D) 5/16
Answer : D

24 What is the probability of getting atleast one head?
(A) 3/4
(B) 5/16
(C) 1/2
(D) 2/9
Answer : A

(25-26): A die is tossed 100 times and the data is recorded in the table.

Outcomes	1	2	3	4	5	6
Frequency	20	15	20	15	20	10

25 What is the probability that we get an even number in a trial?
(A) 0.4
(B) 0.5
(C) 0.3
(D) 0.35
Answer : A

26 What is the probability of getting a number less than 3?
(A) 0.2
(B) 0.25
(C) 0.35
(D) 0.5
Answer : C

27 A dent al survey of 400 students in a school revealed t hat 80 of them had two or more cavities. If the total school enrolment is 1500, about how many student s would you expect to have two or more cavities?
(A) 300
(B) 800
(C) 500
(D) 600
Answer : A

28 The most recent freshman class at Loyola consists of 880 students. Of these, 500
identified themselves as "smokers':
Compute the empirical probability that a randomly select ed freshman student from this class is not a "smoker':
(A) 8/22
(B) 19/44
(C) 15/44
(D) 9/44
Answer : B

29 If the probability of winning a game is 0.35, what is the probability of losing it?
(A) 0.55
(B) 0.75
(C) 0.65
(D) 0.56
Answer : C

30 There are 50 students in a class and their annual result is presented in the given table.

Result	Fail	Pass
No. of Students	7	43

If a student is selected at random, find the probability that the student has passed the examination.
(A) 0.85
(B) 0.68
(C) 0.86
(D) 0.76
Answer : C

31 If P (E) = 0.37, find P (not E).
(A) - 0.37
(B) 0.73
(C) -0.73
(D) 0.63
Answer : D

32 1000 tickets of a lottery were sold and there are 5 prizes on these tickets. If Monu has purchased one lottery ticket, what is her probability of winning a prize?
(A) 0.005
(B) 0.75
(C) 0.055
(D) 0.5
Answer : A

33 When at humbt ack is tossed, there are two possible out comes. If the empirical probability of" point up" is fixed to be 0.73, what should be the probability of"point down"?
(A) 0.37
(B) 0.20
(C) 0.27
(D) 0.51
Answer : C

34 A die is thrown once. What is the probability of getting a number 4 or 5?
(A) 2/3
(B) 1/3
(C) 1/6
(D) 1/2
Answer : B

35 A boy tosses a coin 1000 times and finds that it comes up tail 453 times. Find the probability of getting up head.
(A) 0.457
(B) 0.453
(C) 0.574
(D) 0.547
Answer : D

36 In a cricket match, a bat sman hits a sixer 8 times out of 32 balls played. Find the probability that a sixer is not hit in a ball.
(A) 0.75
(B) 0.25
(C) - 0.25
(D) 0.5
Answer : A

37 A coin is tossed 15 times and observed that head comes up 11 times. What is the probability for a tail to come up?
(A) 11/15
(B) 4/15
(C) 15/4
(D) 15/11
Answer : B

38 A die is tossed once. Which of the following is the probability of getting 3?
(A) 1/6
(B) 1/3
(C) 2/6
(D) 4/6
Answer : A

(39-41): Two coins are tossed 90 times and data recorded as given in the table.

Number of heads in a trial	0	1	2
Frequency	10	25	55

39 What is the probability of get ting one head?
(A) 0
(B) 1/9
(C) 11/18
(D) 5/18
Answer : D

40 What is the probability of getting two heads?
(A) 8/9
(B) 11/18
(C) 5/18
(D) 1/9
Answer : B

41 Find the proability of getting atleast one head.
(A) 8/9
(B) 1/9
(C) 5/18
(D) 11/18
Answer : A

42 Find the probability of not getting 1 or 6 in a single t oss of a die.
(A) 1/2
(B) 1/3
(C) 1/6
(D) 2/3
Answer : D

43 A child has a block in the shape of a cube with one letter written on each face as shown.
A    B    C    D    A    E
If the cube is thrown once, what is the probability of getting A?
(A) 1/3
(B) 2/8
(C) 2/5
(D) 2/3
Answer : A

44 A bag contains 3 red balls, 5 black balls and 4 white balls. A ball is drawn at random from t he bag. What is the probability of get ting a black ball?
(A) 1/4
(B) 5/12
(C) 7/12
(D) 1
Answer : B

45 A die is rolled 100 times and the data is recorded as given in the table.

Outcomes	1	2	3	4	5	6
Frequency	22	13	20	10	25	10

Which of the following is the probability of getting an odd number in a trial?
(A)11/50
(B) 1/5
(C) 67/100
(D) 1/4
Answer : C

46 A card is drawn at random from a pack of well shuffled 52 cards. What is the probability of getting a queen of red suit?
(A) 1/26
(B) 1/13
(C) 1/52
(D) 1/14
Answer : A

47 Find the probability that a number selected at random from the numbers 1 to 25 is not a prime number when each of the given numbers is equally likely to be selected.
(A) 9/25
(B) 16/25
(C) 11/25
(D) 6/25
Answer : B

48 Find the probability of throwing an even number with an ordinary six faced die.
(A) 2/3
(B) 3/5
(C) 1/2
(D) 1/3
Answer : C

 

Question : 1500 families with 2 children were selected randomly, and the following data were recorded:

Compute the probability of a family, chosen at random, having
(i) 2 girls (ii) 1 girl (iii) No girl

Also check whether the sum of these probabilities is 1.
Answer:
Total number of families = 475 + 814 + 211
= 1500

 

Question : Three coins are tossed simultaneously 200 times with the following frequencies of different outcomes:

If the three coins are simultaneously tossed again, compute the probability of 2 heads coming up.
Answer:
Number of times 2 heads come up = 72
Total number of times the coins were tossed = 200

Question : A teacher wanted to analyse the performance of two sections of students in a mathematics test of 100 marks. Looking at their performances, she found that a few students got under 20 marks and a few got 70 marks or above. So she decided to group them into intervals of varying sizes as follows: 0 − 20, 20 − 30… 60 − 70, 70 − 100. Then she formed the following table:

(i) Find the probability that a student obtained less than 20 % in the mathematics test.
(ii) Find the probability that a student obtained marks 60 or above.
Answer:
Total number of students = 90
(i) Number of students getting less than 20 % marks in the test = 7
Hence, required P = 7/90  probability,

(ii) Number of students P = 23/90 obtaining marks 60 or above = 15 + 8 = 23 
Hence, required probability,

Question : 

Concentration of SO2 (in ppm)	Number of days (frequency )
0.00 − 0.04	4
0.04 − 0.08	9
0.08 − 0.12	9
0.12 − 0.16	2
0.16 − 0.20	4
0.20 − 0.24	2
Total	30

The above frequency distribution table represents the concentration of sulphur dioxide in the air in parts per million of a certain city for 30 days. Using this table, find the probability of the concentration of sulphur dioxide in the interval 0.12 − 0.16 on any of these days.
Answer:
Number days for which the concentration of sulphur dioxide was in the interval of
0.12 − 0.16 = 2
Total number of days = 30
Hence, required probability, P = 2/30 =1/15

Probability

Q 1 Tom draws a marble from a bag containing 12 marbles.There are 3 red marbles, 4 blue marbles and 5 green marbles, find the probability that he will draw a blue marble.

Q 2 A basket has 5 apples, 10 oranges and 5 bananas. Find the probability of getting out an apple.

Q 3 One card is drawn from a well-shuffled deck of 52 cards then find the probability that the card will be a king.

Q 4 Mr. And Mrs. X stays in a house along with their seven children. The female to male ratio in the family is 1:2. Find the probability that all the children are either boy or girl.

Q 5 The record of a weather station shows that out of the past 200 consecutives days, its weather forecasts were correct 150 times then find the probability that on a given day it was correct .

Q 6 The record of a weather station shows that out of the past 200 consecutives days, its weather forecasts were correct 150 times then find the probability that on a given day it was not correct.

Q 7 A drawer contains 8 red socks, 3 white socks and 5 blue socks. Without looking, Mayank draws out a pair of socks. Find the probability that the pair of socks is white.

Q 8 Two coins are tossed simultaneously 100 times and we get the following outcomes:(i) One head = 20 (ii) Two heads = 50. Find the probability that there is no head.

Q 9 Two coins are tossed simultaneously 100 times and we get the following outcomes:(i) No head = 30 (ii) Two heads = 50. Find the probability that there is only one head.

Q 10 Two coins are tossed simultaneously 100 times and we get the following outcomes:(i) No head = 30 (ii) One head = 20. Find the probability of getting two heads.

Q 11 A coin is tossed 23 times and observed that 10 times head comes up. Find the probability that a tail comes up.

Q 12 A coin is tossed 100 times. It is observed that 60 times head comes up and 40 times tail comes up then find the probability that neither a head nor a tail comes up.

 

Click on link below to download CBSE Class 9 Mathematics Probability Set A