If $A$ and $B$ are two events, then the value of $P((A \cap B^c) \cup (A^c \cap B))$ is

A. $P(A) + P(B) + P(A \cap B)$
B. $P(A) + P(B) - P(A \cap B)$
C. $P(A) + P(B) + 2P(A \cap B)$
D. $P(A) + P(B) - 2P(A \cap B)$

✅ Correct Answer: $P(A) + P(B) - 2P(A \cap B)$

Explanation

Given $P((A \cap B^c) \cup (A^c \cap B))$ This is the symmetric difference $= P(A - B) + P(B - A)$ $= P(A) - P(A \cap B) + P(B) - P(A \cap B)$ $= P(A) + P(B) - 2P(A \cap B)$

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If $A$ and $B$ are two events, then the value of $P((A \cap B^c) \cup (A^c \cap B))$ is | ACME Academy