For a binomial variate X , if n = 4 and P(X=0) = `16/81` then P(X =4) is

Options

A. `(1)/(16)`
B. `(1)/(81)`
C. `(1)/(27)`
D. `(1)/(8)`

Answer

B

Explanation

We have,
`n=4 and P(X=0)=(16)/(81)`
Let p be the probability of success and q that of failure in a trial.
Then,
`P(X=0)=(16)/(81)`
`rArr .^C_(0)q^4=(16)/(81)`
` rArr q^4=((2)/(3))^4rArr q=(2)/(3)rArr p=(1)/(3)`
`therefore P(X=4)=.^4C_(4)p^4q^0=p^4=((1)/(3))^4=(1)/(81)`