Question

For any two events A and B, if `P(barA) = 1/2, P(barB) = 2/3  "and" P(A\capB) = 1/4, "then" P(barA//barB)` equals ______.

Options

• `3/8`

• `8/9`

• `5/8`

• `1/4`

Answer 1

For any two events A and B, if `P(barA) = 1/2, P(barB) = 2/3  "and" P(A\capB) = 1/4, "then" P(barA//barB)` equals `5/8`.

Explanation:

`P(barA) = 1/2, P(barB) = 2/3` and `P(A\capB) = 1/4`

⇒ `P(A) = 1/2; P(B) = 1/3`

We have, `P(A\cupB) = P(A) + P(B) - P(A\capB)`

= `1/2 + 1/3 - 1/4`

= `7/12`

`P(barA/barB) = (P(barA\capbarB))/(P(barB))`

= `(P(bar(A\cupB)))/(P(barB))`

= `(1 - P(A\cupB))/(P(barB))`

= `(1 - 7/12)/(2/3)`

= `5/8`