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) `(1/2,3/4]` (2) `(3/4,(11)/(12)]` (3) `[0,1/2]` (4) `((11)/(12),1]`

Options

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

Answer

D

Explanation

Probability of at least one failure
`=1-"no failure"ge31/32`
`implies1-p^(5)ge31/32`
`impliesp^(5)le1/32`
`impliesp ge1/2`
Also `ple0`
Hence `p in[0,(1)/(2)]`