The probability of any ship return safely to the port is `1/5` . Find the probability that the returning out of `5` ships, at least `3` ships returns safely. It is given that returning ships are independently.

Options

A. `(1)/(31)`
B. `(3)/(52)`
C. `(181)/(3125)`
D. `(184)/(3125)`

Answer

A

Explanation

Here `p =(1)/(5),q= (1-(1)/(5)) =(4)/(5) ` and n=5
`:. ` P( 3 or 4 or 5 successes) =P(3 successes) +P(4 successes) +P(5 successe)
`=.^(5)C_(3).((1)/(5))^(3).((4)/(5))^(2) +.^(5)C_(4).((1)/(5))^(4) .((4)/(5))^(1)+.^(5)C_(5).((1)/(5))^(5)`
`=((32)/(625)+(4)/(625)+(1)/(3125)) =(181)/(3125)`