If $P(A) = \frac{1}{3}, P(B) = \frac{1}{2}$, and $P(A \cup B) = \frac{3}{4}$ find... If $P(A) = \frac{1}{3}, P(B) = \frac{1}{2}$, and $P(A \cup B) = \frac{3}{4}$ Find:
$P(A \cap B),\\  
P(A^\complement \cup B^\complement) \\
P(A^\complement \cap B)$
Here is what I did:
$P(A \cap B) = P(A) + P(B) - P(A \cup B) = \frac{1}{12}$
$P(A^\complement \cup B^\complement) = P( [A \cap B]^\complement ) = 1 - \frac{1}{12} = \frac{11}{12}$ (Not sure if this is correct)
$P(A^\complement \cap B) = ...$ (I'm not quite sure how to approach this)

All is correct. For the last one you'd need:
$$P(A^\complement \cap B) = P(B) - P(A \cap B) = \frac{1}{2} - \frac{1}{12} = \frac{5}{12}$$
Image to help visualize stuff

