Mathematics : Probability

A die is rolled once. Events A and B are:

A: Getting a number ≥ 2.

B: Getting a number ≤ 4.

Show that events A and B are exhaustive.

A coin is tossed thrice. Event A is described as:
Event A: Atmost one head is obtained. Find A'

Consider 5 independent Bernoulliís trials each with a 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

• (1/2, 3/4]

• (3/4, 11/12]

• [0, 1/2]

• [0, 1/2]

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

• 7/55

• 6/55

• 14/55

• 14/55

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

• 3/16

• 7/32

• 7/16

• 7/16

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

•  1/14

• 1/7

• 5/14

• 5/14

The average marks of boys in a class is 52 and that of girls is 42. The average marks of boys and girls combined is 50. The percentage of boys in the class is

• 40

• 20

• 80

• 80