Given P(A) = 1/2, P(B^c) = 5/6, and P(A U B) = 5/12, find P(A intersect B).

Okay, Dany. Let's complete the previous question first, then move on to the new one.

(i) Given $P(A)=\frac{1}{2}$, $P(B^c)=\frac{5}{6}$, and $P(A \cup B)=\frac{5}{12}$.

Step 1: Calculate $P(B)$.

$$P(B) = 1 - P(B^c)$$ $$P(B) = 1 - \frac{5}{6}$$ $$P(B) = \frac{1}{6}$$

a) Find $P(A \cap B)$.

Step 2: Use the Addition Rule for Probability.

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