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Answer: 0.61
## 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.
Author: Nikitesh Somanthe
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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:
A
0.72
B
0.95
C
0.85
D
0.61
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