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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?

Respuesta :

pedrocarratore

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:

[tex]P(+) = P(D) *0.99 + (1-P(D))*0.01\\P(+)=0.005*0.99+0.995*0.01\\P(+)=0.0149[/tex]

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

[tex]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\%[/tex]

The probability is 0.3322 or 33.22%.

The proportion of disease in the people.

The question stated that the part of the people that are given in the table of the community have certain diseases and these diseases are 0.005. The diagnostic tests are available for measuring the probability of the diseases and have produced a result of a signal of 0.99.

Hence the answer is 0.3322 or 33.22 %.

  • The diseased person has a chance of getting a test of 0.99 and if he is not having a disease then the probability of the disease is about the signal of 0.01%. If the person is tested as positive then the chances for the disease are 33.22%.

Learn more about the proportion of people.

brainly.com/question/14894624.