# Show that for any events A and B, P(A) + P(B) 1 P(A \ B) P(A [ B) P(A) + P(B). For each

**Chapter 1, Problem 41**

(choose chapter or problem)

Show that for any events A and B, P(A) + P(B) 1 P(A \ B) P(A [ B) P(A) + P(B). For each of these three inequalities, give a simple criterion for when the inequality is actually an equality (e.g., give a simple condition such that P(A \ B) = P(A [ B) if and only if the condition hol

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