Question

Given that events A and B are independent with P ( A ) = 0.26 P(A)=0.26 and P ( B ∣ A ) = 0.65 P(B∣A)=0.65, determine the value of P ( B ) P(B), rounding to the nearest thousandth, if necessary.

Answer 1

P(B) = 0.65

Explanation:

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

In which

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

is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

They are independent events, which means that . So

Explanation:

Answer 2

P(B) = 0.65

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) = 0.26, P(B|A) = 0.65`

They are independent events, which means that
`P(A \cap B) = P(A)*P(B)`. So

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

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

`P(B) = (0.65P(A))/(P(A))`

`P(B) = 0.65`