Answer: 0.96

## Explanation To find the probability of either event A or event B occurring (P(A ∪ B)), we use the formula: \[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \] ### Given probabilities: - P(A) = 70% = 0.70 - P(B) = 40% = 0.40 - P(B|A) = 20% = 0.20 ### Step 1: Calculate P(A ∩ B) Using the conditional probability formula: \[ P(A \cap B) = P(B|A) \times P(A) = 0.20 \times 0.70 = 0.14 \] ### Step 2: Calculate P(A ∪ B) \[ P(A \cup B) = P(A) + P(B) - P(A \cap B) = 0.70 + 0.40 - 0.14 = 0.96 \] Therefore, the probability of either event A or event B occurring is 0.96 or 96%. **Key concepts:** - **Union probability**: Probability that at least one of the events occurs - **Conditional probability**: P(B|A) represents the probability of B given that A has occurred - **Intersection probability**: P(A ∩ B) represents the probability that both events occur This calculation follows the fundamental probability rule for the union of two events.

Author: LeetQuiz .