Answer-first summary for fast verification
Answer: 0.61
## 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.
Author: Tanishq Prabhu
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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:
A
0.72
B
0.67
C
0.85
D
0.61
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