Probability

1

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:

  1. 12/5
  2. 6
  3. 4
  4. 6/25
2

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

  1. 6/55
  2. 12/55
  3. 14/45
  4. 7/55
3

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

  1. 7/32
  2. 7/16
  3. 7/64
  4. 3/16
4

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

  1. 1/4
  2. 1/8
  3. 1/16
  4. 1/32
5

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

  1. (3/4,11/2]
  2. (11/2,1]
  3. (1/2,3/4]
  4. [0,1/2]
6

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

  1. 2/5
  2. 1/4
  3. 3/8
  4. 1/5
7

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

  1. 880
  2. 879
  3. 629
  4. 630
8

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. 1/7
  2. 1/14
  3. 5/14
  4. 1/50
9

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. 1/5
  2. 2/5
  3. 3/5
  4. 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. Probability that the problem is solved is

  1. 1/3
  2. 1/2
  3. 3/4
  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. The set of possible values of x are in the interval

  1. [1/3, 1/2]
  2. [1/3, 13/3]
  3. [0, 1]
  4. [1/3, 2/3]