Introduction to Probability · Problem 4.1.26

Conditional Probability — Grinstead & Snell

Mathematics — Probability · conditional-probability-inequality

Problem

Suppose that

A

and

B

are events such that

P(A|B) = P(B|A)

and

P(A \cup B) = 1

and

P(A \cap B) > 0

. Prove that

P(A) > 1/2