Question

Consider two events A and B, where \(P(A) \ge 0.9\) and \(P(B) \ge 0.6\). What is the best numerical bound you can get for \(P(A \cap B)\)?

Answer 1

it better be greater than or equal to .5 because
\[P(A\cup B)=P(A)+P(B)-P(A\cap B)\] and any probability has to be less than or equal to 1

Answer 2

Oh so we assume \(P (A\cup B) \) = 1 because this is the largest probability we can assume?