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.