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 $\frac{31}{32}$, then p lies in the interval

Question

( A ) $(\frac{11}{12}, 1]$
( B ) $[0, \frac{1}{2}]$
( C ) $(\frac{1}{2}, \frac{3}{4}]$
( D ) $(\frac{3}{4}, \frac{11}{12}]$