For two events, A and B, it is given that `P(A) = (3)/(5), P(B) = (3)/(10)`, and `P(A|B)= (2)/(3)` . If `bar(A)` and `bar(B)` are the complementary events of A and B, then `P(bar(A) |bar(B))` equal to ?

Options

A. `(3)/(7)`
B. `(3)/(4)`
C. `(1)/(3)`
D. `(4)/(7)`

Answer

A

Explanation

` P(A) = (3)/(5) , P (B) = (3)/(10)`
`rArr P(bar(B)) = 1- - P(B) = (7)/(10)`
`P ((A)/(B)) = (2)/(3)`
`rArr P((A)/(B)) = (P(Ann B))/(P(B)) = (2)/(3)`
`rArr P(A nn B) = (2)/(3) xx (3)/(10) = (1)/(5)`
` P (A nnB) = P(A) +P(B) - P(A nn B)`
`rArr P(A nnB) = (3)/(5) +(3)/(10)-(1)/(5) = (7)/(10)`
`rArr bar(A nnB) = 1 -(7)/(10) = (3)/(10)`
`rArrP((bar(A))/(bar(B))) =(P(bar(A) nnbar(B)))/(P(bar(B)))= ((3)/(10))/((7)/(10)) = (3)/(10) xx (10)/(7)`
`rArr P((bar(A))/(bar(B))) = (3)/(7)`