1
###
A box contains 15 green and 10 yellow balls. If 10 balls are randomly drawn

A box contains 15 green and 10 yellow balls. If 10 balls are randomly drawn, one-by-one, with replacement, then the variance of the number of green balls drawn is:

- 12/5
- 6
- 4
- 6/25

2
###
If two different numbers are taken from the set

If two different numbers are taken from the set {0, 1, 2, 3,..., 10}; then the probability that their sum as well as absolute difference are both multiple of 4, is

- 6/55
- 12/55
- 14/45
- 7/55

3
###
For three events A, B and C, P(Exactly one of A or B occurs)

For three events A, B and 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) = 1/4 and P(All the three events occur simultaneously) = 1/16. Then the probability that at least one of the events occurs, is

- 7/32
- 7/16
- 7/64
- 3/16

4
###
The mean and variance of a random variable X having binomial

The mean and variance of a random variable X having binomial distribution are 4 and 2 respectively, then P (X = 1) is

- 1/4
- 1/8
- 1/16
- 1/32

5
###
Consider 5 independent Bernoullí's trials each with probability

Consider 5 independent Bernoulli's trials each with probability of success P. If the probability of at least one failure is greater than or equal to 31/32, then P lies in the interval

- (3/4,11/2]
- (11/2,1]
- (1/2,3/4]
- [0,1/2]

6
###
Three numbers are chosen at random without replacement

Three numbers are chosen at random without replacement from {1, 2, 3,...... 8}. The probability that their minimum is 3, given that their maximum is 6, is

- 2/5
- 1/4
- 3/8
- 1/5

7
###
Assuming the balls to be identical except for difference in colours

Assuming the balls to be identical except for difference in colours, the number of ways in which one or more balls can be selected from 10 white, 9 green and 7 black balls is

- 880
- 879
- 629
- 630

8
###
One ticket is selected at random from 50 tickets numbered

One ticket is selected at random from 50 tickets numbered 00, 01, 02,... , 49. Then the probability that the sum of the digits on the selected ticket is 8, given that the product of these digits is zero, equals

- 1/7
- 1/14
- 5/14
- 1/50

9
###
Five horses are in a race. Mr.A selects two of the horses

Five horses are in a race. Mr.A selects two of the horses at random and bets on them. The probability that Mr.A selected the winning horse is

- 1/5
- 2/5
- 3/5
- 4/5

10
###
A problem in mathematics is given to three students A, B, C and their respective probability of solving the problem is 1/2, 1/3 and 1/4

A problem in mathematics is given to three students A, B, C and their respective probability of solving the problem is 1/2, 1/3 and 1/4. Probability that the problem is solved is

- 1/3
- 1/2
- 3/4
- 2/3

11
###
Events A, B, C are mutually exclusive events such that P(A) = (3x + 1)/3, P(B) = (x - 1)/4, P(C) = (1 - 2x)/4

Events A, B, C are mutually exclusive events such that P(A) = (3x + 1)/3, P(B) = (x - 1)/4, P(C) = (1 - 2x)/4. The set of possible values of x are in the interval

- [1/3, 1/2]
- [1/3, 13/3]
- [0, 1]
- [1/3, 2/3]