Financial Risk Manager Part 1

Explanation

To calculate the probability of a positive test, we use the law of total probability:

Let's define the events:

• + = positive diagnosis
• - = negative diagnosis
• H = heart disease
• H' = no heart disease

Given probabilities:

• P(+|H) = 0.95 (probability of positive test given heart disease)
• P(-|H') = 0.99 (probability of negative test given no heart disease)
• P(H) = 0.25 (probability of heart disease)
• P(H') = 0.75 (probability of no heart disease)

First, we need P(+|H') = 1 - P(-|H') = 1 - 0.99 = 0.01

Using the law of total probability:

P(+) = P(+|H) × P(H) + P(+|H') × P(H')

P(+) = (0.95 × 0.25) + (0.01 × 0.75)

P(+) = 0.2375 + 0.0075 = 0.245

Therefore, the probability of a positive test is 0.245, which corresponds to option C.