Question

Let A and B be two events. Suppose the probabilities P(A) = 0.5, P(

A and B) = 0.2
and P((AUB)') = 0.4. What is P(B)?​

Answer 1

`P(B) = 0.3`

Explanation:

We use the following formula for Venn probabilities to solve this question.

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

P((AUB)') = 0.4

This means that:

`P(A \cup B) = 1 - P(A \cup B)' = 1 - 0.4 = 0.6`

We also have that:

`P(A) = 0.5, P(A \cap B) = 0.2`

What is P(B)?​

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

`0.6 = 0.5 + P(B) - 0.2`

`0.3 + P(B) = 0.6`

`P(B) = 0.3`