Consider 5 independent Bernoulli's trials each with probability of at least one failure is greater than or equal to `31/32,` then p lies in the interval

Options

A. `((1)/(2),(3)/(4)]`
B. `((3)/(4),(11)/(12)]`
C. `[0,(1)/(2)]`
D. `((11)/(12),1]`

Answer

C

Explanation

Let X denote the number of failures in 5 trials.
Then, `P(X=r)=.^5C_(r)(1-p)^rp^5-r,r=0,1,2,.....,5`.
`therefore P(Xgt1)ge (31)/(32)`
`rArr 1-P(X=0)ge (31)/(32)`
`rArr 1-p^5ge (31)/(32)rArr (1)/(32)ge p^5rArr p lt (1)/(2)rArr p in [0,1//2]`