For two mutually exclusive events A and B, P(A) = 0.2 and `P(bar(A) CB) = 0.3`. What is `P(A|(Auu B))` equal to ?

Options

A. `(1)/(2)`
B. `(2)/(5)`
C. `(2)/(7)`
D. `(2)/(3)`

Answer

B

Explanation

Events A and B are mutually excusive.
Hence ` P (A nnB) = phi = 0`
`therefore P (A nn B) = P(A) + P(B)" "....(i)`
`P(A) = 0.2" "["given"]`
` P(B) = P(bar(A)nn B) + P(A nnB)`
`P(B) = P(bar(A) nnB) " "[becauseP(A nn B) = 0]`
= 0.3
`P(A nn B) = 0.2 + 0.3 = 0.5`
` P(A|A nn B) = (P(A))/(P(Auu B)) = (0.2)/(0.5) = (2)/(5)`
`P(A|(AuuB))=(2)/(5)`