Prove or disprove：Pr(A)=Pr(B)=p Pr(A∩B)≤p^2

Answer 1

False. The easiest counterexample is A = B, 0 < p < 1

Then, P(AB) = p and p > p² for 0 < p < 1, as p - p² = p(1 - p) > 0.