Question

Let’s suppose that a physician comes across someone who exhibits symptoms of a particular disease. The disease is relatively rare and it affects 4 out of every 1,000 people. Let’s also assume that the screening test that the physician recommends costs $500 and requires a blood sample. Given that the test is expensive, the patient wants to know the probability of disease, given a positive test result. The test is widely used and the probability of screening positive given the presence of the disease is 85%. In addition, the test comes back positive 10% of the time and negative 90% of the time. From the scenario described above, what is the

probability of being screen positive and having the disease?
a. 85%
b. 90%
c. 10%
d. Not known

Answer 1

To find the probability of being screen positive and having the disease, use the concept of conditional probability.

Step-by-step explanation:

To find the probability of being screen positive and having the disease, we can use the concept of conditional probability. Let D represent the event that a person has the disease, and P+ represent the event that a person tests positive.

The probability of disease given a positive test result can be calculated using the formula: P(D|P+) = (P(P+|D) × P(D)) / P(P+).

In this case, we are given that P(P+|D) = 0.85, P(D) = 0.004, and P(P+) = 0.10. Substituting these values into the formula, we get:

P(D|P+) = (0.85 × 0.004) / 0.10 = 0.034.

Therefore, the probability of being screen positive and having the disease is 3.4%.