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. In a given population, 45% of people are considered high risk for a heart attack, (25% have high cholesterol, 30% have high blood pressure). If a randomly selected person has high blood pressure, what is the probability they also have high cholesterol?
Other
Community
NNikitesh
A
15%
B
20%
C
25%
D
33%
Explanation:
The correct answer is 33%.
Step-by-step explanation:
-
Given probabilities:
- P(High Risk) = P(A ∪ B) = 45% = 0.45
- P(High Cholesterol) = P(A) = 25% = 0.25
- P(High Blood Pressure) = P(B) = 30% = 0.30
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Find P(A ∩ B) using the union formula: P(A ∪ B) = P(A) + P(B) - P(A ∩ B) 0.45 = 0.25 + 0.30 - P(A ∩ B) 0.45 = 0.55 - P(A ∩ B) P(A ∩ B) = 0.55 - 0.45 = 0.10
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Calculate conditional probability: We need P(High Cholesterol | High Blood Pressure) = P(A|B) P(A|B) = P(A ∩ B) / P(B) P(A|B) = 0.10 / 0.30 = 1/3 ≈ 0.3333 = 33.33%
Interpretation: Given that a person has high blood pressure, there's a 33% chance they also have high cholesterol.
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