Question

Jason discovers that the probability that he has heart disease is 0.85. The accuracy rate to test for heart disease is 0.95. The test predicts that Jason has heart disease. What is the probability that Jason has heart disease, given the outcome of the test?

A) 0.85.
B) 0.95.
C) 0.89.
D) 0.90.

Answer 1

The probability that Jason has heart disease, given the outcome of the test, is approximately 0.9902.

Step-by-step explanation:

To find the probability that Jason has heart disease, given the outcome of the test, we can use Bayes' theorem.

Let H = Jason has heart disease, T = the test predicts that Jason has heart disease.

We are given P(H) = 0.85 (the probability that Jason has heart disease) and P(T|H) = 0.95 (the accuracy rate of the test).

Bayes' theorem states that: P(H|T) = (P(T|H) * P(H)) / P(T).

The probability of the test predicting that Jason has heart disease, P(T), can be calculated as follows:

P(T) = P(T|H) * P(H) + P(T|H') * P(H') = 0.95 * 0.85 + 0.05 * (1 - 0.85) = 0.95 * 0.85 + 0.05 * 0.15 = 0.8075 + 0.0075 = 0.815.

Now we can substitute the values into Bayes' theorem:

P(H|T) = (0.95 * 0.85) / 0.815 = 0.8075 / 0.815 ≈ 0.9902.

Therefore, the probability that Jason has heart disease, given the outcome of the test, is approximately 0.9902.