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 and the two events are independent. In a given population, 25% have high cholesterol and 30% have high blood pressure. If a randomly selected person has high blood pressure, what is the probability they also have high cholesterol?
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TTanishq
A
15%
B
20%
C
25%
D
33%
Explanation:
Explanation
Given that the two events (high cholesterol and high blood pressure) are independent, the probability of having high cholesterol given that the person has high blood pressure is simply the marginal probability of having high cholesterol.
Key Concepts:
- Independence: Two events A and B are independent if P(A|B) = P(A)
- Here, A = "has high cholesterol" and B = "has high blood pressure"
- P(A) = 0.25 (25%)
- P(B) = 0.30 (30%)
Calculation:
Since the events are independent: P(high cholesterol | high blood pressure) = P(high cholesterol) = 0.25 = 25%
Why other options are incorrect:
- A. 15%: This would be P(A ∩ B) = 0.25 × 0.30 = 7.5%, not 15%
- B. 20%: No mathematical basis for this value
- D. 33%: This would be P(A|B) = P(A∩B)/P(B) = (0.25×0.30)/0.30 = 0.25 = 25%, not 33%
The independence assumption is crucial here - it means that knowing someone has high blood pressure doesn't change the probability that they also have high cholesterol.
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