How do I go about answering the following question.
Given two events A,B with (A) = 3/4 and P(B) = 1/3, what is the smallest possible value of P(A $\cap$ B)? The largest? That is, a and b such that, $$a \leq P(A \cap B) \leq b,$$ holds and any value in the closed interval [a,b] is possible.
a = ? b = ?
Below is a image of what I think is the shaded area of interest. Is this correct? If so, then is the probability 1/4 x 2/3 = 1/6. In which case, a = 1/4 and b = 2/3?