In a Binominal distribution, the mean is three times its variance. What is the probality to exactly 3 successes out of 4 trials?

Options

A. `(80)/(243)`
B. `(40)/(243)`
C. `(20)/(243)`
D. `(10)/(243)`

Answer

A

Explanation

Mean = np
Variance = npq
Given, np = 3np q
`rArr q=(1)/(3),p=(2)/(3)`.
Also, Given n = 5 trials.
r = 3
we know, `p(x=r)=.^(n)c_(r).p^(r).q^(n-r)`
`p(x=3)=.^(5)c_(3)((2)/(3))^(3)((1)/(3))^(2)`
`=(80)/(243).`