The proportion of people in a given community who have a certain disease is 0.005. A test is available to diagnose the disease. If a person

Question

The proportion of people in a given community who have a certain disease is 0.005. 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 0.99. If a person does not have the disease, the probability that the test will produce a positive signal is 0.01.
If a person tests positive, what is the probability that the person actually has the disease?

in progress 0
Ivy 4 weeks 2021-12-29T07:44:17+00:00 1 Answer 0 views 0

Answers ( )

    0
    2021-12-29T07:46:15+00:00

    Answer:

    0.3322 or 33.22%

    Step-by-step explanation:

    The probability that the person has the disease, P(D), is 0.005

    The probability that a person tests positive P(+) is:

    P(+) = P(D) *0.99 + (1-P(D))*0.01\\P(+)=0.005*0.99+0.995*0.01\\P(+)=0.0149

    Given that the test is positive, the probability that the person actually has the disease is determined by:

    P(D|P)=\frac{P(D)*0.99}{P(+)}\\P(D|P)=\frac{0.005*0.99}{0.0149}\\P(D|P)=0.3322=33.22\%

    The probability is 0.3322 or 33.22%.

Leave an answer

45:7+7-4:2-5:5*4+35:2 =? ( )