A man can hit a bird once in 3 shots . On this assumption he fires 3 shots . What is the chance that at least one bird is hit ?

Answer

`(19)/(27)`

Explanation

`p=(1)/(3),q=(1-(1)/(3))=(2)/(3) " and " n=3`
`P(X=r) =.^(n)C_(r ).p^(r ).q^((n-r)) =.^(3)C_(r ).((1)/(3))^(r ) .((2)/(3))^((3-r))`
`=[.^(3)C_(1)xx(1)/(3)xx((2)/(3))^(2)]+[.^(3)C_(2)xx((1)/(3))^(2)xx(2)/(3)] +[.^(3)C_(3)xx((1)/(3))^(3)]`
`=((4)/(9) +(2)/(9)+(1)/(9))=(7)/(9)`