In a binomail distribution , then mean is `(2)/(3)` and the variance is `(5)/(9)`. What is the probability that `X = 2?`.

Options

A. `(5)/(36)`
B. `(25)/(36)`
C. `(25)/(216)`
D. `(25)/(54)`

Answer

C

Explanation

`P(A)=(1)/(3),P(B)=(1)/(6),(A cap B)=(1)/(12)`
`P(B|overset(_)A)=(P(Bcapoverset(_)A))/(P(overset(_)A))`
Now, `P(Bcap overset(_)A)=P(B)-P(A capoverset(_)B)=(1)/(6)-(1)/(12)=(1)/(12)`
`P(overset(_)A)=1-(1)/(3)=(2)/(3)`
`P(B|overset(_)A)=((1)/(12))/((2)/(3))=(1)/(12)xx(3)/(2)=(1)/(8)`