question_answer

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

A)  \[\left. \left( \frac{3}{4},\,\,\frac{11}{12} \right. \right]\]                

B)  \[\left[ 0,\,\,\frac{1}{2} \right]\]

C)  \[\left. \left( \frac{11}{12},\,\,1 \right. \right]\]                   

D)  \[\left. \left( \frac{1}{2},\,\,\frac{3}{4} \right. \right]\]

E)  None of these