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If in a binomial distribution n=4,\ P(X=...

If in a binomial distribution `n=4,\ P(X=0)=(16)/(81),\ t h e n\ P(X=4)` equals `1/(16)` b. `1/(81)` c. `1/(27)` d. `1/8`

A

`(1)/(16)`

B

`(1)/(81)`

C

`(1)/(27)`

D

`(1)/(8)`

Text Solution

Verified by Experts

The correct Answer is:
B
(b) Given , n=4 and P(X=0)`=(16)/(81)`
Let p be the probability of succes and q be the probability of failure in a trial.
Than, `" "P(X=0)=(16)/(81)`
`rArr " " ""^(4)C_(0)p^(0)q^(4)=(16)/(81)`
`rArr " " q^(4)=((2)/(3))^(4) rArr q=(2)/(3)`
`rArr " " p=(1)/(3)`
`:. " " P(X=4)=""^(4)C_(4)p^(4)q^(0)=p^(4)=((1)/(3))^(4)=(1)/(81)`
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