Question

According to the general equation for conditional probability, if P(A^B)= 2/3 and P(B)= 3/4, what is P(A|B)?

A. 15/16
B. 24/25
C. 8/9
D. 35/36

Answer 1

C)P(A|B) =
`(8)/(9)`.

Explanation:

Given : P(A^B)= 2/3 and P(B)= 3/4.

TO find : what is P(A|B).

Solution : We have given that P(A^B)= 2/3 and P(B)= 3/4.

By the conditional probability :

P(A|B) =
`(P(A\ and\ B))/(P(B))`.

Plugging the values

P(A|B) =
`(P(A\ and\ B))/(P(B))`.

P(A|B) =
`((2)/(3))/((3)/(4))`.

P(A|B) =
`(8)/(9)`.

Therefore, C)P(A|B) =
`(8)/(9)`.

Answer 2

C. 8/9 because if you do 2/3 divided by 3/4 then that gives you 8/9.