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Page 1
PROBABILITY ASSIGNMENT
1. A positive integer is chosen at random. The probability that sum of the digits of its square is 33 is :
(A) 1/11 (B) 1/33
(C) 2/33 (D) None of these
2. Two persons A and B appear in an interview for two vacancies. If the probability of their selection are 1/4 and 1/6
respectively, then probabilities that none of them is selected is :
(A) 1/24 (B) 5/12
(C) 5/8 (D) 19/12
3. A bag contains 5 brown and 4 white socks. A man pulls out two socks. The probability that they are in the same
colour is :
(A) 5/108 (B) 1/6
(C) 5/18 (D) 4/9
4. Tickets are numbered 1 to 100. They are well–shuffled and a ticket is drawn at random. Probability that the drawn
ticket has a number 5 or a multiple of 5 is :
(A) 1/10 (B) 1/5
(C) 1/25 (D) 1/2
5. Out of 13 applicants for a job, there are 5 women and 8 men. It is desired to select 2 persons for the job.
The probability that at least one of the selected persons will be woman is :
(A) 25/39 (B) 14/39
(C) 5/13 (D) 10/13
6. From a well shuffled pack of playing cards, two cards are drawn one by one with replacement. The probability that
both are aces is :
(A) 2/13 (B) 1/51
(C) 1/221 (D) None of these
7. Three coins are tossed together. The probability of atleast two heads is :
(A) 1/8 (B) 3/8
(C) 1/2 (D) 1/4
8. Two dice are thrown simultaneously. The probability of obtaining a total score of 5 is
(A) 1/18 (B) 1/12
(C) 1/9 (D) none of these
9. The probabilities of solving a problem by three students A, B, C are 1/2, 1/3, 1/4 respectively. The probability that
the problem will be solved is
(A) 1/4 (B) 1/2
(C) 3/4 (D) 1/3
10. The probability that a leap year selected at random contains 53 Sundays is
(A) 7/366 (B) 26/183
(C) 1/7 (D) 2/7
GIITJEE CHANDIGARH LIMITED SCO 382, Sector 37–D, Chandigarh – 160 036 Ph: 3290959 P – 1
Page 2
PROBABILITY ASSIGNMENT
1. A positive integer is chosen at random. The probability that sum of the digits of its square is 33 is :
(A) 1/11 (B) 1/33
(C) 2/33 (D) None of these
2. Two persons A and B appear in an interview for two vacancies. If the probability of their selection are 1/4 and 1/6
respectively, then probabilities that none of them is selected is :
(A) 1/24 (B) 5/12
(C) 5/8 (D) 19/12
3. A bag contains 5 brown and 4 white socks. A man pulls out two socks. The probability that they are in the same
colour is :
(A) 5/108 (B) 1/6
(C) 5/18 (D) 4/9
4. Tickets are numbered 1 to 100. They are well–shuffled and a ticket is drawn at random. Probability that the drawn
ticket has a number 5 or a multiple of 5 is :
(A) 1/10 (B) 1/5
(C) 1/25 (D) 1/2
5. Out of 13 applicants for a job, there are 5 women and 8 men. It is desired to select 2 persons for the job.
The probability that at least one of the selected persons will be woman is :
(A) 25/39 (B) 14/39
(C) 5/13 (D) 10/13
6. From a well shuffled pack of playing cards, two cards are drawn one by one with replacement. The probability that
both are aces is :
(A) 2/13 (B) 1/51
(C) 1/221 (D) None of these
7. Three coins are tossed together. The probability of atleast two heads is :
(A) 1/8 (B) 3/8
(C) 1/2 (D) 1/4
8. Two dice are thrown simultaneously. The probability of obtaining a total score of 5 is
(A) 1/18 (B) 1/12
(C) 1/9 (D) none of these
9. The probabilities of solving a problem by three students A, B, C are 1/2, 1/3, 1/4 respectively. The probability that
the problem will be solved is
(A) 1/4 (B) 1/2
(C) 3/4 (D) 1/3
10. The probability that a leap year selected at random contains 53 Sundays is
(A) 7/366 (B) 26/183
(C) 1/7 (D) 2/7
GIITJEE CHANDIGARH LIMITED SCO 382, Sector 37–D, Chandigarh – 160 036 Ph: 3290959 P – 1
11. A bag contains 3 red, 4 white and 5 blue balls. All balls are different. Two balls are drawn at random.
The probability that they are of different colour is
(A) 47/66 (B) 10/33
(C) 5/22 (D) none of these
12. Three identical dice are rolled. The probability that the same number will appear on each of them is
(A) 1/6 (B) 1/18
(C) 1/36 (D) none of these
13. The probability that a man aged 50 years will die in a year is p. The probability that out of n men A
1
, A
2
, …., A
n
each aged 50 years, A
1
will die and be first to die is
(A) 1 – (1 – p)
n
(B) [1 – (1 – p)
n
] / n
2
(C) [1 – (1 – p)
n
] / n (D) none of these
14. A bag contains 3 white and 4 red balls. Another bag contains 5 white and 7 red balls. A ball is taken out of the first
bag and put in to the second. A ball is then taken out of the second bag. The probability that it is a red ball is
(A) 1/3 (B) 53/91
(C) 32/91 (D) none of these
15. A bag contains 10 mangoes out of which 4 are rotten, two mangoes are taken out together. If one of them is
found to be good, the probability that other is also good is
(A) 1/3 (B) 8/15
(C) 5/13 (D) 2/3
16. A card is drawn at random from a pack of 100 cards numbered 1 to 100. The probability of drawing a number
which is a square is
(A) 1/5 (B) 2/5
(C) 1/10 (D) none of these
17. The probability of India winning a test match against West Indies is 1/2. Assuming independence from match to
match the probability that in a 5 match series India's second win occurs at the third test is
(A) 1/8 (B) 1/4
(C) 1/2 (D) 2/3
18. The probability that at least one of the events A and B occurs is 0.7 and they occur simultaneously with probability
0.2. Then P( A ) + P( B ) =
(A) 1.8 (B) 0.6
(C) 1.1 (D) 1.4
19. Both A and B throw a dice. The chance that B throws a number higher than that thrown by A is
(A) 1/2 (B) 21/36
(C) 15/36 (D) none of these
20. The probability that a man can hit a target is 3/4. He tries 5 times. The probability that he will hit the target at least
three times is
(A) 291/364 (B) 371/464
(C) 471/502 (D) 459/512
GIITJEE CHANDIGARH LIMITED SCO 382, Sector 37–D, Chandigarh – 160 036 Ph: 3290959 P – 2
Page 3
PROBABILITY ASSIGNMENT
1. A positive integer is chosen at random. The probability that sum of the digits of its square is 33 is :
(A) 1/11 (B) 1/33
(C) 2/33 (D) None of these
2. Two persons A and B appear in an interview for two vacancies. If the probability of their selection are 1/4 and 1/6
respectively, then probabilities that none of them is selected is :
(A) 1/24 (B) 5/12
(C) 5/8 (D) 19/12
3. A bag contains 5 brown and 4 white socks. A man pulls out two socks. The probability that they are in the same
colour is :
(A) 5/108 (B) 1/6
(C) 5/18 (D) 4/9
4. Tickets are numbered 1 to 100. They are well–shuffled and a ticket is drawn at random. Probability that the drawn
ticket has a number 5 or a multiple of 5 is :
(A) 1/10 (B) 1/5
(C) 1/25 (D) 1/2
5. Out of 13 applicants for a job, there are 5 women and 8 men. It is desired to select 2 persons for the job.
The probability that at least one of the selected persons will be woman is :
(A) 25/39 (B) 14/39
(C) 5/13 (D) 10/13
6. From a well shuffled pack of playing cards, two cards are drawn one by one with replacement. The probability that
both are aces is :
(A) 2/13 (B) 1/51
(C) 1/221 (D) None of these
7. Three coins are tossed together. The probability of atleast two heads is :
(A) 1/8 (B) 3/8
(C) 1/2 (D) 1/4
8. Two dice are thrown simultaneously. The probability of obtaining a total score of 5 is
(A) 1/18 (B) 1/12
(C) 1/9 (D) none of these
9. The probabilities of solving a problem by three students A, B, C are 1/2, 1/3, 1/4 respectively. The probability that
the problem will be solved is
(A) 1/4 (B) 1/2
(C) 3/4 (D) 1/3
10. The probability that a leap year selected at random contains 53 Sundays is
(A) 7/366 (B) 26/183
(C) 1/7 (D) 2/7
GIITJEE CHANDIGARH LIMITED SCO 382, Sector 37–D, Chandigarh – 160 036 Ph: 3290959 P – 1
11. A bag contains 3 red, 4 white and 5 blue balls. All balls are different. Two balls are drawn at random.
The probability that they are of different colour is
(A) 47/66 (B) 10/33
(C) 5/22 (D) none of these
12. Three identical dice are rolled. The probability that the same number will appear on each of them is
(A) 1/6 (B) 1/18
(C) 1/36 (D) none of these
13. The probability that a man aged 50 years will die in a year is p. The probability that out of n men A
1
, A
2
, …., A
n
each aged 50 years, A
1
will die and be first to die is
(A) 1 – (1 – p)
n
(B) [1 – (1 – p)
n
] / n
2
(C) [1 – (1 – p)
n
] / n (D) none of these
14. A bag contains 3 white and 4 red balls. Another bag contains 5 white and 7 red balls. A ball is taken out of the first
bag and put in to the second. A ball is then taken out of the second bag. The probability that it is a red ball is
(A) 1/3 (B) 53/91
(C) 32/91 (D) none of these
15. A bag contains 10 mangoes out of which 4 are rotten, two mangoes are taken out together. If one of them is
found to be good, the probability that other is also good is
(A) 1/3 (B) 8/15
(C) 5/13 (D) 2/3
16. A card is drawn at random from a pack of 100 cards numbered 1 to 100. The probability of drawing a number
which is a square is
(A) 1/5 (B) 2/5
(C) 1/10 (D) none of these
17. The probability of India winning a test match against West Indies is 1/2. Assuming independence from match to
match the probability that in a 5 match series India's second win occurs at the third test is
(A) 1/8 (B) 1/4
(C) 1/2 (D) 2/3
18. The probability that at least one of the events A and B occurs is 0.7 and they occur simultaneously with probability
0.2. Then P( A ) + P( B ) =
(A) 1.8 (B) 0.6
(C) 1.1 (D) 1.4
19. Both A and B throw a dice. The chance that B throws a number higher than that thrown by A is
(A) 1/2 (B) 21/36
(C) 15/36 (D) none of these
20. The probability that a man can hit a target is 3/4. He tries 5 times. The probability that he will hit the target at least
three times is
(A) 291/364 (B) 371/464
(C) 471/502 (D) 459/512
GIITJEE CHANDIGARH LIMITED SCO 382, Sector 37–D, Chandigarh – 160 036 Ph: 3290959 P – 2
21. The probability that a person will hit a target in shooting practice is 0.3. If he shoots 10 times, the probability that
he hits the target is
(A) 1 (B) 1 – (0.7)
10
(C) (0.7)
10
(D) (0.3)
10
22. A and B are two independent events. The probability that both A and B occur is 1/6 and the probability that neither
of them occurs is 1/3. Then
(A) P (A) = 1/2, P (B) = 1/3 (B) P (A) = 1/2, P (B) = 1/6
(C) P (A) = 1/3, P (B) = 1/2 (D) none of these
23. In a class of 125 students 70 passed in Mathematics, 55 in Statistics and 30 in both. The probability that a student
selected at random from the class, has passed in only one subject is
(A) 13/25 (B) 3/25
(C) 17/25 (D) 8/25
24. A lot consists of 12 good pencils, 6 with minor defects and 2 with major defects. A pencil is chosen at random.
The probability that this pencil is not defective is
(A) 3/5 (B) 3/10
(C) 4/5 (D) 1/2
25. 3 mangoes and 3 apples are in a box. If 2 fruits are chosen at random, the probability that one is a mango and the
other is an apple is
(A) 3/5 (B) 5/6
(C) 1/36 (D) none of these
26. A father has 3 children with at least one boy. The probability that he has 2 boys and one girl is
(A) 1/4 (B) 1/3
(C) 2/3 (D) none of these
27. Out of 13 applicants for a job, there are 5 women and 8 men. It is desired to select 2 persons for the job.
The probability that at least one of the selected persons will be a woman is
(A) 25/39 (B) 14/39
(C) 5/13 (D) 10/13
28. Two events A and B have probability 0.25 and 0.50. The probability that both occur simultaneously is 0.14.
The probability that neither A nor B occurs is
(A) 0.75 (B) 0.61
(C) 0.39 (D) none of these
29. If A and B are independent events and P (A ? B) = 9/10, P (B) = 4/10, then P (A) =
(A) 1/6 (B) 5/6
(C) 1/9 (D) none of these
30. A, B, C in order toss a coin. The first one to throw a head wins. Assuming the game continues indefinite their
respective chances of winning the game are
(A) 4/7, 2/7, 1/7 (B) 1/7, 4/7, 2/7
(C) 2/7, 4/7, 1/7 (D) none of these
GIITJEE CHANDIGARH LIMITED SCO 382, Sector 37–D, Chandigarh – 160 036 Ph: 3290959 P – 3
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FAQs on MCQ Probability ( With Answers ) - Class 11
| 1. What is the definition of probability in the context of statistics? |  |
Ans. In statistics, probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.
| 2. How is probability calculated in a simple event? | |
Ans. In a simple event, where all outcomes are equally likely, the probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
| 3. What is the difference between theoretical probability and experimental probability? | |
Ans. Theoretical probability is based on mathematical calculations and assumptions, while experimental probability is determined through actual repeated trials or experiments. Theoretical probability is often used in ideal situations, while experimental probability is used when dealing with real-world scenarios.
| 4. Can the probability of an event be greater than 1? | |
Ans. No, the probability of an event cannot be greater than 1. A probability of 1 represents a certain event, meaning it is guaranteed to occur, while a probability greater than 1 would imply a higher certainty than absolute certainty, which is not possible.
| 5. How do you calculate the probability of multiple independent events occurring together? | |
Ans. To calculate the probability of multiple independent events occurring together, you multiply the probabilities of each individual event. This is known as the multiplication rule of probability.
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