Probability (Class 12)

If A and B are two events such that P(A) = 0.7, P(B) = 0.4 and P(A B) = 0.5, where B denotes the complement of B, then P (B (A B) ) is equal to

1. 13
2. 12
3. 14
4. 16

A bag contains 19 unbiased coins and one coin with head on both sides. One coin drawn at random is tossed and head turns up. If the probability that the drawn coin was unbiased, is mn, (m, n) = 1, then n2 - m2 is equal to :

1. 64
2. 80
3. 60
4. 72

Let a random variable X take values 0, 1, 2, 3 with P(X = 0) = P(X = 1) = p, P(X = 2) = P(X = 3) and E(X2) = 2E(X). Then the value of 8p - 1 is :

1. 2
2. 0
3. 3
4. 1

A box contains 10 pens of which 3 are defective. A sample of 2 pens is drawn at random and let X denote the number of defective pens. Then the variance of X is

1. 1115
2. 215
3. 35
4. 2875

A card from a pack of 52 cards is lost. From the remaining 51 cards, n cards are drawn and are found to be spades. If the probability of the lost card to be a spade is 1150, then n is equal to .

If the probability that the random variable X takes the value x is given by P(X = x) = k(x + 1)3-x, x = 0, 1, 2, 3, , where k is a constant, then P(X 3) is equal to

1. 19
2. 827
3. 727
4. 49

Given three identical bags each containing 10 balls, whose colours are as follows : arraylccc & Red & Blue & Green \ Bag I & 3 & 2 & 5 \ Bag II & 4 & 3 & 3 \ Bag III & 5 & 1 & 4 array A person chooses a bag at random and takes out a ball. If the ball is Red, the probability that it is from bag I is p and if the ball is Green, the probability that it is from bag III is q, then the value of ( 1p + 1q ) is:

1. 6
2. 9
3. 7
4. 8

Let A = [aij] be a 2 2 matrix such that aij \0, 1\ for all i and j. Let the random variable X denote the possible values of the determinant of the matrix A. Then, the variance of X is:

1. 58
2. 14
3. 34
4. 38

Bag 1 contains 4 white balls and 5 black balls, and Bag 2 contains n white balls and 3 black balls. One ball is drawn randomly from Bag 1 and transferred to Bag 2. A ball is then drawn randomly from Bag 2. If the probability, that the ball drawn is white, is 2945, then n is equal to:

1. 5
2. 6
3. 4
4. 3

Three defective oranges are accidentally mixed with seven good ones and on looking at them, it is not possible to differentiate between them. Two oranges are drawn at random from the lot. If x denotes the number of defective oranges, then the variance of x is

1. 26/75
2. 14/25
3. 18/25
4. 28/75