Financial Risk Manager Part 1

Explanation

This is a conditional probability problem that can be solved using Bayes' Theorem and set theory principles.

Given Information:

• P(High Risk) = P(High Cholesterol ∪ High Blood Pressure) = 45% = 0.45
• P(High Cholesterol) = 25% = 0.25
• P(High Blood Pressure) = 30% = 0.30

Step 1: Find P(Both)

Using the formula for union of two events: $P(A \cup B) = P(A) + P(B) - P(A \cap B)$

Substitute the known values: $`$0.45 = 0.25 + 0.30 - P(A \cap B)$$ $$0.45` = 0.55 - P(A \cap B)$$P(A \cap B) = 0.55 - 0.45 = 0.10$$

Step 2: Calculate Conditional Probability

We want P(High Cholesterol | High Blood Pressure): $P(\text{High Cholesterol} \mid \text{High Blood Pressure}) = \frac{P(\text{Both})}{P(\text{High Blood Pressure})}$

$P(\text{High Cholesterol} \mid \text{High Blood Pressure}) = \frac{0.10}{0.30} = \frac{1}{3} = 33.33\%$

Therefore, if a randomly selected person has high blood pressure, there is a 33% probability they also have high cholesterol.

Answer: D (33%)