Consider 5 independent Bernoullí's trials each with probability

• 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

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

Answer

1 - P⁵ ≥ 31/32

P⁵ ≤ 1/32

P ≤ 1/2

The correct option is D.