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 probabilty of success and failure are p and q respectively.
`therefore p=2q and p+q=1`
`implies 3q=1 implies q=(1)/(3) and p=(2)/(3)`
`therefore ` Required probability =P(Four success)+P(Five success)+P(Six success)
`=""^(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)`