Answer-first summary for fast verification
Answer: 0.245
## Explanation To find the probability of an economic downturn **and** negative sales growth, we need to use the multiplication rule for joint probability: **Step 1: Identify the relevant probabilities** - Probability of economic downturn = 0.35 - Probability of negative sales growth **given** economic downturn = 0.70 (from the table: -10% sales growth with probability 0.70 in downturn scenario) **Step 2: Calculate joint probability** Joint probability = P(Economic downturn) × P(Negative sales growth | Economic downturn) = 0.35 × 0.70 = 0.245 **Step 3: Verify calculation** 0.35 × 0.70 = 0.245 **Step 4: Match to options** 0.245 corresponds to option C. **Key Concept**: This is a joint probability calculation using conditional probability. The probability of two events A and B occurring together is P(A and B) = P(A) × P(B|A), where P(B|A) is the conditional probability of B given A has occurred.
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An analyst considers the following scenarios for the economy and the sales growth of a company:
| Scenario | Probability of Scenario | Sales Growth | Probability of Sales Growth |
|---|---|---|---|
| Economic boom | 0.65 | 15% | 0.70 |
| -5% | 0.30 | ||
| Economic downturn | 0.35 | 4% | 0.30 |
| -10% | 0.70 |
Based on this information, the probability of an economic downturn and negative sales growth is closest to:
A
0.195
B
0.210
C
0.245
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