Question

P(A) = 20%. P(B) = 50%. P(BIA) = P(B). What is P(A and B)?

Answer 1

P(A and B) = 0.1 = 10%

Explanation:

Conditional Probability

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, we have that:

`P(A) = 0.2, P(B|A) = 0.5`

What is P(A and B)?

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

`P(A \cap B) = P(B|A)*P(A) = 0.5*0.2 = 0.1`

P(A and B) = 0.1 = 10%