Financial Risk Manager Part 1
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A patient is considered high risk for a heart attack if they either have high cholesterol or high blood pressure. What percentage of patients are NOT considered high risk for a heart attack if 25% have high cholesterol, 30% have high blood pressure and 10% have both high cholesterol and high blood pressure?
Explanation:
Explanation
This is a probability problem involving non-mutually exclusive events (since patients can have both conditions).
Given:
- P(High Cholesterol) = 25% = 0.25
- P(High Blood Pressure) = 30% = 0.30
- P(Both) = 10% = 0.10
Step 1: Calculate P(High Risk) Using the formula for non-mutually exclusive events: P(A ∪ B) = P(A) + P(B) - P(A ∩ B) P(High Risk) = 0.25 + 0.30 - 0.10 = 0.45 or 45%
Step 2: Calculate P(Not High Risk) P(Not High Risk) = 1 - P(High Risk) = 1 - 0.45 = 0.55 or 55%
Verification:
- Only high cholesterol: 25% - 10% = 15%
- Only high blood pressure: 30% - 10% = 20%
- Both conditions: 10%
- Neither condition: 100% - (15% + 20% + 10%) = 55%
The correct answer is 55% (Option C).