A man throws a die until he gets a number greater than `3`. The probability that he gets `5` in the last throw

Options

A. `1//3`
B. `1//4`
C. `1//6`
D. `1//36`

Answer

A

Explanation

`(a)` At event `A` he gets a number greater than `3`
`:.P(A)=1//2`
At event `B` he gets `5` in last throw
`:.P(B)=1//6`
`:.` Required probability is
`P(E)=(1)/(6)+(1)/(2)*(1)/(6)+(1)/(2)*(1)/(2)*(1)/(6)+…..oo`
`=((1)/(6))/(1-(1)/(2))=(1)/(3)`