Question

Given that events A and B are independent with P(A)=0.24P(A)=0.24 and P(B|A)=0.85P(B∣A)=0.85, determine the value of P(B)P(B), rounding to the nearest thousandth, if necessary.

Answer 1

P(B) = 0.85

Explanation:

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

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

In which

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

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

P(A) is the probability of A happening.

In this question:

`P(A) = 0.24, P(B|A) = 0.85`

These events are independent.

This means that
`P(A \cap B) = P(A)*P(B)`. So

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

`P(B|A) = (P(A)*P(B))/(P(A))`

`P(B|A) = P(B)`

So

`P(B) = 0.85`