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 price will decrease in price is closest to:
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A
0.72
B
0.67
C
0.85
D
0.61
Explanation:
Explanation
To solve this probability problem, we use the addition rule of probability:
[ P(A \cup B) = P(A) + P(B) - P(A \cap B) ]
Where:
- ( A ) = event that ABX announces negative quarterly results
- ( B ) = event that stock price decreases
Given:
- ( P(A) = 0.40 ) (40% chance of negative results)
- ( P(B) = 0.55 ) (55% chance stock decreases)
- ( P(B|A) = 0.85 ) (85% chance stock decreases given negative results)
Step 1: Calculate ( P(A \cap B) ) [ P(A \cap B) = P(B|A) \times P(A) = 0.85 \times 0.40 = 0.34 ]
Step 2: Apply the addition rule [ P(A \cup B) = P(A) + P(B) - P(A \cap B) = 0.40 + 0.55 - 0.34 = 0.61 ]
Therefore, the probability that ABX will announce negative quarterly results OR the stock price will decrease is 0.61.
Verification:
- The answer makes sense because it's greater than either individual probability but less than their sum (which would be 0.95 without subtracting the overlap).
- The overlap ( P(A \cap B) = 0.34 ) represents the joint probability of both events occurring.
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