$P(A) = 0.6$ and $P(B) = 0.7$. What is the least possible value of $P(A \cap B)$?

Explanation

1. 01

   $P(A \cup B) = P(A) + P(B) - P(A \cap B) = 1.3 - P(A \cap B)$.

2. 02

   $P(A \cup B) \le 1$, so $P(A \cap B) \ge 0.3$: the events must overlap by at least 0.3.