Question

What is the P(A and B) given that P(A) = 0.53, P(B) = 0.39, and P(A or B) = 0.48

Answer 1

P(A and B) = 0.44

Explanation:

Venn probabilities:

Suppose that we have two events, A and B. The probability of A and B is:

`P(A \cap B) = P(A) + P(B) - P(A \cup B)`

In which
`P(A \cup B)` is P(A or B).

In this question:

`P(A) = 0.53, P(B) = 0.39, P(A \cup B) = 0.48`

Then

`P(A \cap B) = P(A) + P(B) - P(A \cup B) = 0.53 + 0.39 - 0.48 = 0.44`

So

P(A and B) = 0.44