If in a trial the probability of success is twice the probability of failure. In six trials the probability of at least four successes is

Options

A. `(496)/(729)`
B. `(400)/(729)`
C. `(500)/(729)`
D. `(600)/(729)`

Answer

A

Explanation

Let the probability of success and failur are p and q respectively.
`therefore p = 2 q and p + q = 1`
`rArr 3q = 1 rArr q = (1)/(3) and p =(2)/(3)`
`therefore ` Required probability
`=""^(6)C_(4)((2)/(3))^(4) ((1)/(3))^(2) = ""^(6)C_(5)((2)/(3))^(5) ((1)/(3)) + ""^(6)C_(6)((2)/(3))^(6)`
`=(240)/(729) + (192)/(729)+ (64)/(729) = (496)/(729)`