Answer: 0.245

## 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.

Author: Tanishq Prabhu