26.Suppose that A and B are events that P(A|B) = P(B|A) and P(A\(\cup\)B) = 1 and P(A\(\cap\) B) > 0. Prove that P(A) > \(\frac{1}{2}\).
\(\because\) P(A\(\cap\)B) = P(A|B)P(B) = P(B|A)P(A), P(A|B) = P(B|A), P(A\(\cap\)B)$$0,
\(\therefore\) P(A) = P(B).
\(\because\) P (A \(\cup\) B) = P (A) + P (B) - P (A \(\cap\) B), P(A\(\cup\)B) = 1,
\(\therefore\) 2P(A) - P(A\(\cap\)B) = 1.
\(\because\) P(A\(\cap\)B) > 0,
\(\therefore\) 2P(A) > 1,
\(\therefore\) P(A) > \(\frac{1}{2}\).