1.

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)`

Answer» Correct Answer - B
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)`


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