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Answer: 25%
## 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.
Author: Tanishq Prabhu
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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?
A
15%
B
20%
C
25%
D
33%