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Consider 5 independent Bernoulli's trial...

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

A

`((11)/(12),1]`

B

`((1)/(2),(3)/(4)]`

C

`((3)/(4),(11)/(12)]`

D

`[0,(1)/(2)]`

Text Solution

Verified by Experts

The correct Answer is:
D
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)]`
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