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 ?

A [1, 32]

B (0, 1)

C [1, 1/2]

D (1, 1/2]

Correct Answer: Option C

Probability of atleast one failure
= 1 - no failure > 31/32
= 1 -\(P^5\) > 31/32

= \(P^5\) < 1/32
= p < 1/2
Also p > 0
Hence p lies in [0,1/2].