The correct answer is A (0.58).

Explanation:

This is a probability question involving the union of two events. The formula for the probability of either event A or event B occurring is:

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

Where:

• P(A) = probability of Apple's share price declining by more than 5% = 0.4
• P(B) = probability of Microsoft's share price declining by more than 5% = 0.3
• P(A ∩ B) = probability that both Apple and Microsoft share prices decline by more than 5%

Assuming the events are independent (which is reasonable for two different companies), we can calculate: P(A ∩ B) = P(A) × P(B) = 0.4 × 0.3 = 0.12

Therefore: P(A ∪ B) = 0.4 + 0.3 - 0.12 = 0.58

Why other options are incorrect:

• B (0.12): This is the probability that both events occur (intersection), not either event (union).
• C (0.7): This would be the sum of probabilities (0.4 + 0.3) without subtracting the intersection, which double-counts the scenario where both events occur.
• D (0.67): This is not the correct calculation for the union of independent events.

Key Concept: When calculating the probability of either of two events occurring, you must subtract the probability that both occur to avoid double-counting that scenario.