If `A` and `B` are any two events such that `P(A)=2/5` and `P(AnnB)=3/20` then the conditional probability `P(A|(A'uuB'))` where `A'` denotes the complement of `A` is equal to

Options

A. `(8)/(17)`
B. `(1)/(4)`
C. `(5)/(17)`
D. `(11)/(20)`

Answer

C

Explanation

We have,
`P(A)=(2)/(3) " and " P(A cap B)=(3)/(20)`
`therefore P(A//A' cup B)=(P(A cap (A' cup B')))/(P(A' cup B'))=(P((A cup A') cup (A cap B')))/(P(A' cup B'))`
`=(P(phi cup (A cap B')))/(P(A' cup B'))=(P(A cap B'))/(1-P(A cap B))=(P(A)-(A cap B))/(1-P(A cap B))`
`=((2)/(5)-(3)/(20))/((17)/(20))=(5)/(17)`