Question

According to the general equation for conditional probability, if P(A, B) =4/7

and P(B) =7/8 - what is P(AIB)?

Answer 1

`P(A|B) = (32)/(49)`

Explanation:

We use the conditional probability formula to solve this question. It is

`P(A|B) = (P(A \cap B))/(P(B))`

In which

P(A|B) is the probability of event A happening, given that B happened.

`P(A \cap B)` is the probability of both A and B happening.

P(B) is the probability of B happening.

We have that:

`P(A \cap B) = (4)/(7), P(B) = (7)/(8)`

So

`P(A|B) = (P(A \cap B))/(P(B)) = ((4)/(7))/((7)/(8)) = (4)/(7)*(8)/(7) = (32)/(49)`

Then

`P(A|B) = (32)/(49)`