Mathematics

When events are independent, knowing one happened tells you nothing about the other — so $P(A \cap B) = P(A) \cdot P(B)$. The key is using the union formula $P(A \cup B) = P(A) + P(B) - P(A \cap B)$ and substituting the independence condition to create an equation in one unknown. Solve for $P(A)$ by treating it as an algebra problem.

When events are independent, knowing one happened tells you nothing about the other — so $P(A \cap B) = P(A) \cdot P(B)$. The key is using the union formula $P(A \cup B) = P(A) + P(B) - P(A \cap B)$ and substituting the independence condition to create an equation in one unknown. Solve for $P(A)$ by treating it as an algebra problem.