Problem
Given $P(A)=0.4, P(B)=0.5$, and $P(A \cup B)=0.6$, a. find $P(A \cap B)$.
Solution
Step 1 ：Given $P(A)=0.4, P(B)=0.5$, and $P(A \cup B)=0.6$, we can use the formula for the probability of the union of two events: $P(A \cup B) = P(A) + P(B) - P(A \cap B)$. We are given $P(A)$, $P(B)$, and $P(A \cup B)$, so we can solve for $P(A \cap B)$.
Step 2 ：Using the formula, we get $P(A \cap B) = 0.4 + 0.5 - 0.6 = 0.3$. Therefore, the final answer is \(\boxed{0.3}\).
