MCQ Probability ( With Answers ) Class 11 Notes | EduRev

Created by: Sahil Setia

Class 11 : MCQ Probability ( With Answers ) Class 11 Notes | EduRev

 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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