Question

If events A and B are mutually exclusive, P(A or B) = 0.5, and P(B) = 0.3; then what is P(A)?

Answer 1

Answer:

$P(A) = 0.2$

Step-by-step explanation:

We have that:

$P(A) = P(a) + P(A \cap B)$

In which P(a) is the probability of a but not b and $P(A \cap B)$ is the probability of both A and B.

By the same logic, we have that:

$P(B) = P(b) + P(A \cap B)$

Also

P(A or B) is

$P(A \cup B) = P(a) + P(b) + P(A \cap B)$

Events A and B are mutually exclusive

This means that $P(A \cap B) = 0$

$P(B) = 0.3 = P(b)$

$P(A \cup B) = P(a) + P(b) + P(A \cap B)$

$0.5 = P(a) + 0.3$

$P(a) = 0.2$

$P(A) = P(a) + P(A \cap B) = 0.2 + 0 = 0.2$