1. **State the problem:** We are given two independent events A and B with probabilities $P(A) = 0.82$ and $P(B) = 0.60$. We need to find the probability of both events occurring together, denoted as $P(A \cap B)$. 2. **Formula for independent events:** For two independent events, the probability of both events occurring is the product of their individual probabilities: $$P(A \cap B) = P(A) \times P(B)$$ 3. **Apply the formula:** Substitute the given values: $$P(A \cap B) = 0.82 \times 0.60$$ 4. **Calculate the product:** $$P(A \cap B) = 0.492$$ 5. **Interpretation:** The probability that both events A and B occur is 0.492, or 49.2%.