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To solve this problem, we need to find the probabilities \( P(A \cap B) \) and \( P(A \cup B) \), given that \( A \) and \( B \) are independent events with \( P(A) = 0.60 \) and \( P(B) = 0.50 \).

### Step-by-Step Solution

1. **Find \( P(A \cap B) \):**
   Since \( A \) and \( B \) are independent, the probability of their intersection is given by the product of their individual probabilities:
   \[
   P(A \cap B) = P(A) \times P(B)
   \]
   Substituting the given values:
   \[
   P(A \cap B) = 0.60 \times 0.50 = 0.30
   \]

2. **Find \( P(A \cup B) \):**
   The probability of the union of two events is given by:
   \[
   P(A \cup B) = P(A) + P(B) - P(A \cap B)
   \]
   Using the values we have:
   \[
   P(A \cup B) = 0.60 + 0.50 - 0.30 = 0.80
   \]

### Summary
- \( P(A \cap B) = 0.30 \)
- \( P(A \cup B) = 0.80 \)

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### Related Questions
1. What is the probability of \( P(\overline{A}) \)?
2. How do we calculate \( P(\overline{A} \cap B) \) using the given information?
3. If \( P(A) \) was different, how would it affect \( P(A \cap B) \) and \( P(A \cup B) \)?
4. How do we verify the independence of two events?
5. What is the relationship between mutually exclusive and independent events?

### Tip
When dealing with probabilities, always check if events are independent or mutually exclusive, as it significantly affects how you calculate the combined probabilities.

Supongamos que A y B son sucesos independientes tal que P(A) = 0.60 y P(B) = 0.50. Hallar P(A ∩ B) y P(A ∪ B).

Learn how to calculate the intersection and union of independent events in probability, using the given probabilities P(A) = 0.60 and P(B) = 0.50. This problem covers essential probability rules including the multiplication rule and the addition rule.

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