Mathematics

Problem

If two events (A) and (B) are mutually exclusive, then (a)

(P(A \cap B) = 0)

(b)

(P(A \cup B) = 0)

(c)

(P(A|B) = 1)

(d)

(P(A) = P(B))

Intuitive explanation

Mutually exclusive events cannot happen at the same time—they have no overlap. The key insight is that if $A$ and $B$ can't both occur, their intersection must be empty, which immediately tells you what their probability must be. Think about what "no overlap" means for the probability of $A$ and $B$ happening together.

Intuitive explanation

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