Financial Risk Manager Part 1
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There is a 40% chance that ABX will announce negative quarterly results tomorrow. On any given day, there is a 55% chance that the company's stock price will decrease. If negative quarterly results are announced, the probability that the stock price will decline is 85%. Tomorrow, the probability that ABX will announce negative quarterly results or that the stock will decrease in price is closest to:
Other
Community
NNikitesh
A
0.72
B
0.95
C
0.85
D
0.61
Explanation:
Explanation
This is a probability problem using the formula for the union of two events:
Given:
- P(Negative Results) = 0.40
- P(Price Decline) = 0.55
- P(Price Decline | Negative Results) = 0.85
Formula for union of two events: P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
First, we need to find P(A ∩ B): P(Price Decline ∩ Negative Results) = P(Negative Results) × P(Price Decline | Negative Results) = 0.40 × 0.85 = 0.34
Now apply the union formula: P(Negative Results ∪ Price Decline) = P(Negative Results) + P(Price Decline) - P(Negative Results ∩ Price Decline) = 0.40 + 0.55 - 0.34 = 0.61
Alternative calculation (as shown in the text): 0.4 + 0.55 - (0.4 × 0.85) = 0.95 - 0.34 = 0.61
Why not simply add probabilities? Because there's overlap between the events - when negative results are announced, there's an 85% chance of price decline, so we need to avoid double-counting this intersection.
Key concepts:
- Conditional probability: P(A|B) = P(A∩B)/P(B)
- Union probability formula: P(A∪B) = P(A) + P(B) - P(A∩B)
- The intersection represents the probability that both events occur simultaneously.
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