1 
Two events A and B have probabilities 0.25 and 0.50 respectively. The possibility of both A and B occur simultaneously is 0.14 then the probability that neither A nor B occur is a) 0.39 b) 0.25 c) 0.11 d) None of these
Two events A and B have probabilities 0.25 and 0.50 respectively. The possibility of both A and B occur simultaneously is 0.14 then the probability that neither A nor B occur is a) 0.39 b) 0.25 c) 0.11 d) None of these

IIT 1980 
02:08 min

2 
The probability that an event A happens in one of the experiments is 0.4 Three independent trials of these experiments are performed. The probability that the event A happens at least once is a) 0.936 b) 0.784 c) 0.904 d) None of these
The probability that an event A happens in one of the experiments is 0.4 Three independent trials of these experiments are performed. The probability that the event A happens at least once is a) 0.936 b) 0.784 c) 0.904 d) None of these

IIT 1980 
02:34 min

3 
If A and B are two independent events such that P (A) > 0 and P (B) ≠ 1 then is equal to a) b) c) d)
If A and B are two independent events such that P (A) > 0 and P (B) ≠ 1 then is equal to a) b) c) d)

IIT 1980 

4 
Fifteen coupons are numbered 1, 2, 3, . . . ., 15 respectively. Seven coupons are selected at random one at a time with replacement. The probability that the largest number appearing on a selected coupon is 9 is a) b) c) d) None of these
Fifteen coupons are numbered 1, 2, 3, . . . ., 15 respectively. Seven coupons are selected at random one at a time with replacement. The probability that the largest number appearing on a selected coupon is 9 is a) b) c) d) None of these

IIT 1983 

5 
Three identical dice are rolled. The probability that the same number will appear on each of them is a) b) c) d)
Three identical dice are rolled. The probability that the same number will appear on each of them is a) b) c) d)

IIT 1984 
01:22 min

6 
A box contains 24 identical balls of which 12 are white and 12 are black. The balls are drawn at random from the box one at a time with replacement. The probability that a white ball is drawn for the fourth time on the seventh draw is a) b) c) d)
A box contains 24 identical balls of which 12 are white and 12 are black. The balls are drawn at random from the box one at a time with replacement. The probability that a white ball is drawn for the fourth time on the seventh draw is a) b) c) d)

IIT 1984 

7 
The probability that at least one of the events A and B occurs is 0.6. If A and B occur simultaneously with probability 0.2 then is a) 0.4 b) 0.8 c) 1.2 d) 1.4
The probability that at least one of the events A and B occurs is 0.6. If A and B occur simultaneously with probability 0.2 then is a) 0.4 b) 0.8 c) 1.2 d) 1.4

IIT 1987 
02:39 min

8 
India played two matches each with Australia and West indies. In any match the probability of India getting the points 0, 1, and 2 are 0.45, 0.05 and 0.50 respectively. Assuming that the outcomes are independent, the probability of India getting at least seven points is a) 0.8730 b) 0.0875 c) 0.0625 d) 0.0250
India played two matches each with Australia and West indies. In any match the probability of India getting the points 0, 1, and 2 are 0.45, 0.05 and 0.50 respectively. Assuming that the outcomes are independent, the probability of India getting at least seven points is a) 0.8730 b) 0.0875 c) 0.0625 d) 0.0250

IIT 1992 
03:03 min

9 
An unbiased die with faces marked 1, 2, 3, 4, 5 and 6 is rolled 4 times. Out of four face values obtained, the probability that the minimum face value is not less than 2 and the maximum face value is not greater than 5 is a) 16/81 b) 1/81 c) 80/81 d) 65/81
An unbiased die with faces marked 1, 2, 3, 4, 5 and 6 is rolled 4 times. Out of four face values obtained, the probability that the minimum face value is not less than 2 and the maximum face value is not greater than 5 is a) 16/81 b) 1/81 c) 80/81 d) 65/81

IIT 1993 
01:57 min

10 
Let A, B , C be three mutually independent events. Consider the two statements S_{1} and S_{2} S_{1} : A and B ∪ Care independent S_{2 } : A and B ∩ C are independent. Then a) Both S_{1} and S_{2} are true b) Only S_{1} is true c) Only S_{2 }is true d) Neither S_{1} nor S_{2 }is true
Let A, B , C be three mutually independent events. Consider the two statements S_{1} and S_{2} S_{1} : A and B ∪ Care independent S_{2 } : A and B ∩ C are independent. Then a) Both S_{1} and S_{2} are true b) Only S_{1} is true c) Only S_{2 }is true d) Neither S_{1} nor S_{2 }is true

IIT 1994 

11 
The probability of India winning a test match against West Indies is ½. Assuming independence of outcomes in each match, the probability that in a 5 test match series India’s second win will occur in the third test is a) b) c) d)
The probability of India winning a test match against West Indies is ½. Assuming independence of outcomes in each match, the probability that in a 5 test match series India’s second win will occur in the third test is a) b) c) d)

IIT 1995 
02:40 min

12 
Three of the vertices of a regular hexagon are chosen at random. The probability that the triangle with three vertices is equilateral equals a) b) c) d)
Three of the vertices of a regular hexagon are chosen at random. The probability that the triangle with three vertices is equilateral equals a) b) c) d)

IIT 1995 
02:30 min

13 
For the three events A, B, C, P(exactly one of A or B occurs) = P(exactly one of B or C occurs) = P(exactly one of C or A occurs) = p and P(all the three events occur simultaneously = where . Then the probability of at least one of A, B, C occurring is a) b) c) d)
For the three events A, B, C, P(exactly one of A or B occurs) = P(exactly one of B or C occurs) = P(exactly one of C or A occurs) = p and P(all the three events occur simultaneously = where . Then the probability of at least one of A, B, C occurring is a) b) c) d)

IIT 1996 
06:23 min

14 
Seven white balls and three black balls are randomly placed in a row. The possibility that no two black balls are placed adjacently equals a) b) c) d)
Seven white balls and three black balls are randomly placed in a row. The possibility that no two black balls are placed adjacently equals a) b) c) d)

IIT 1998 
03:25 min

15 
If from each of the three boxes containing 3 white and one black; 2 white and 2 black; 1 white and 3 black balls, one ball is drawn at random then the probability that 2 white and 1 black ball will be drawn is a) b) c) d)
If from each of the three boxes containing 3 white and one black; 2 white and 2 black; 1 white and 3 black balls, one ball is drawn at random then the probability that 2 white and 1 black ball will be drawn is a) b) c) d)

IIT 1998 
02:35 min

16 
If are complementary events E and F respectively and if 0 < p(E) < 1, then a) b) c) d)
If are complementary events E and F respectively and if 0 < p(E) < 1, then a) b) c) d)

IIT 1998 
01:47 min

17 
If E and F are events with P (E) ≤ P (F) and P (E ∩ F) > 0 then a) occurrence of E ⇒ occurrence of F b) occurrence of F ⇒ occurrence of E c) nonoccurrence of E ⇒ nonoccurrence of F d) none of the above occurrences hold
If E and F are events with P (E) ≤ P (F) and P (E ∩ F) > 0 then a) occurrence of E ⇒ occurrence of F b) occurrence of F ⇒ occurrence of E c) nonoccurrence of E ⇒ nonoccurrence of F d) none of the above occurrences hold

IIT 1998 

18 
A fair coin is tossed repeatedly. If the tail appears on first four times, then the probability of the head appearing on in the fifth toss equals a) b) c) d)
A fair coin is tossed repeatedly. If the tail appears on first four times, then the probability of the head appearing on in the fifth toss equals a) b) c) d)

IIT 1998 
00:47 min

19 
If the integers m and n are chosen at random between 1 and 100 then the probability that a number of form is divisible by 5, equals a) b) c) d)
If the integers m and n are chosen at random between 1 and 100 then the probability that a number of form is divisible by 5, equals a) b) c) d)

IIT 1999 

20 
The numbers are selected from the set S = {1, 2, 3, 4, 5, 6} without replacement one by one. Probability that the minimum of the two numbers is less than 4 is a) b) c) d)
The numbers are selected from the set S = {1, 2, 3, 4, 5, 6} without replacement one by one. Probability that the minimum of the two numbers is less than 4 is a) b) c) d)

IIT 2003 
03:06 min

21 
If three distinct numbers are chosen randomly from the first 100 natural numbers then the probability that all three of them are divisible by 2 and 3 is a) b) c) d)
If three distinct numbers are chosen randomly from the first 100 natural numbers then the probability that all three of them are divisible by 2 and 3 is a) b) c) d)

IIT 2003 
03:45 min

22 
If P (B) = and then P (B ∩ C) is a) b) c) d)
If P (B) = and then P (B ∩ C) is a) b) c) d)

IIT 2004 
02:56 min

23 
A fair die is rolled. The probability that 1 occurs at the even number of trail is a) b) c) d)
A fair die is rolled. The probability that 1 occurs at the even number of trail is a) b) c) d)

IIT 2005 
05:00 min

24 
One Indian and four American men and their wives are to be seated randomly around a circular table. Then the conditional probability that Indian man is seated adjacent to his wife given that each American man is seated adjacent to his wife is a) b) c) d)
One Indian and four American men and their wives are to be seated randomly around a circular table. Then the conditional probability that Indian man is seated adjacent to his wife given that each American man is seated adjacent to his wife is a) b) c) d)

IIT 2007 
09:20 min

25 
Let ^{ }denotes the complement of an event E. Let E, F, G are pair wise independent events with P (G) > 0 and P (E ∩ F ∩ G) = 0 then equals a) b) c) d)
Let ^{ }denotes the complement of an event E. Let E, F, G are pair wise independent events with P (G) > 0 and P (E ∩ F ∩ G) = 0 then equals a) b) c) d)

IIT 2007 
