Question

In: Math

The proportion of people in a given community who have a certain disease is 0.01. A...

The proportion of people in a given community who have a certain disease is 0.01. A test is available to diagnose the disease. If a person has the disease, the probability that the test will produce a positive signal is 0.95. If a person does not have the disease, the probability that the test will produce a positive signal is 0.02.

a.Given that the test is positive, what is the probability that the person has the disease?

b.Given that the test is negative, what is the probability that the person does not have the disease?

c.For many medical tests, it is standard procedure to repeat the test when a positive signal is given. Assume that repeated medical tests are independent. What is the probability that the person has the disease given that two independent tests are positive?

Expert Solution

Let D shows the event that person has disease so we have

Let P shows the event that test gives positive result and N shows the event that test gives negative result. So we have

By the complement rule we have

a)

By the Baye's theorem the required probability is

Answer: 0.3242

b)

By the Baye's theorem the required probability is

Answer: 0.9998

c)

Since each time the probability that test give positive result remain same and each test is independent from other so we have

The probability that the person has the disease given that two independent tests are positive is

Answer: 0.95797

milcah answered 1 year ago

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