# Question(s) from Search: IIT

All BasicClass XI-XII ExamsIIT JEE
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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 S1 and S2

S1 : A and B ∪ Care independent

S2  : A and B ∩ C are independent. Then

a) Both S1 and S2 are true

b) Only S1 is true

c) Only S2 is true

d) Neither S1 nor S2 is true

Let A, B , C be three mutually independent events. Consider the two statements S1 and S2

S1 : A and B ∪ Care independent

S2  : A and B ∩ C are independent. Then

a) Both S1 and S2 are true

b) Only S1 is true

c) Only S2 is true

d) Neither S1 nor S2 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) non-occurrence of E ⇒ non-occurrence 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) non-occurrence of E ⇒ non-occurrence 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

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