Probability (Class 12)

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

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

A and B alternately throw a pair of dice. A wins if he throws a sum of 5 before B throws a sum of 8, and B wins if he throws a sum of 8 before A throws a sum of 5. The probability, that A wins if A makes the first throw, is

1. 819
2. 919
3. 817
4. 917

A coin is tossed three times. Let X denote the number of times a tail follows a head. If and 2 denote the mean and variance of X, then the value of 64 ( + 2 ) is:

1. 64
2. 32
3. 51
4. 48

Two balls are selected at random one by one without replacement from a bag containing 4 white and 6 black balls. If the probability that the first selected ball is black, given that the second selected ball is also black, is mn, where (m,n)=1, then m+n is equal to :

1. 4
2. 14
3. 11
4. 13

If A and B are two events such that P(A B)=0.1, and P(A B) and P(B A) are the roots of the equation 12x2-7x+1=0, then the value of P( A B)P( A B) is :

1. 43
2. 74
3. 94
4. 53

Three balls are drawn at random from a bag containing 5 blue and 4 yellow balls. Let the random variables X and Y respectively denote the number of blue and yellow balls. If X and Y are the means of X and Y respectively, then 7 X + 4 Y is equal to .