Probability (Class 12) · Question 15

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

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

Bag B1 contains 6 white and 4 blue balls, Bag B2 contains 4 white and 6 blue balls, and Bag B3 contains 5 white and 5 blue balls. One of the bags is selected at random and a ball is drawn from it. If the ball is white, then the probability that the ball is drawn from Bag B2 is:

1. 25
2. 415
3. 13
4. 23