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

Suppose a population A has 100 observations 101, 102, … , 200, and another population B has 100 observations 151, 152, … , 250. If VA and VB represent the variances of the two populations, respectively, then V_A/V_B is 

• 1

• 9/4

• 4/9

• 4/9

7.

At an election, a voter may vote for any number of candidates, not greater than the number to be elected. There are 10 candidates and 4 are of be elected. If a voter votes for at least one candidate, then the number of ways in which he can vote is

• 5040

• 6210

• 385

• 385

The probability that A speaks truth is 4/ 5 , while this probability for B is 3/ 4 . The probability that they contradict each other when asked to speak on a fact is

• 3/20

• 1/20

• 7/20

• 7/20

From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. The number of such arrangements is

• At least 750 but less than 1000

• At least 1000

• Less then 500

• At least 500 but less than 750

The probability that a non-leap year selected at random will have 53 Sunday is,

• 0

• 1/7

• 2/7

• 3/7