Weekend Rain Bounds via Frechet-Hoeffding

Let $A$ be the event "rain on Saturday" with $P(A) = p$, and let $B$ be the event "rain on Sunday" with $P(B) = q$. You know the marginal probabilities but nothing about the joint distribution. 1. Using the Frechet-Hoeffding bounds, determine the tight range for $P(A \cap B)$. 2. Suppose you are told that "rain usually lasts at least two days." Without assuming independence, argue whether $P(A \cap B)$ tends toward the upper or lower end of that range, and explain why. 3. Now suppose instead that "rain rarely lasts more than one day." Argue the direction of $P(A \cap B)$ within the range and explain your reasoning.