Tagged: lower bound

Lower and Upper Bounds of the Probability of the Intersection of Two Events

Problem 741

Let $A, B$ be events with probabilities $P(A)=2/5$, $P(B)=5/6$, respectively. Find the best lower and upper bound of the probability $P(A \cap B)$ of the intersection $A \cap B$. Namely, find real numbers $a, b$ such that
\[a \leq P(A \cap B) \leq b\] and $P(A \cap B)$ could take any values between $a$ and $b$.

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