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## Homework Statement

Consider events A, B, and C such that P (A) = P (B) = P (C) = 0.2, A and C are mutually exclusive, B and C are mutually exclusive, and P (A ∪ B ∪ C) = 0.5. Give the value of P (A ∩ B), providing justiﬁcation for your answer.

## Homework Equations

## The Attempt at a Solution

If A & C and B & C are mutually exclusive, and if P(A U B U C) = 0.5, then P(A U B) = 0.3. And if P(A) = P(B) = 0.2, then

**P(A ∩ B) = 0.1**.