Financial Risk Manager Part 1
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An investor owns shares of both Apple and Microsoft. He assumes that the probability of Apple's share price declining by more than 5% this year is 0.4 while the probability of Microsoft's share price declining by more than 5% is 0.3. What is the probability that either Apple or Microsoft share prices will decline in price by more than 5% this year?
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Community
NNikitesh
A
0.58
B
0.12
C
0.7
D
0.67
Explanation:
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.
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