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.