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**Aryth** Suppose there is a medical diagnostic test for a disease. The sensitivity of the test is .95. This means that if a person has the disease, the probability that the test gives a positive response is .95. The specificity of the test is .90. This means that if a person does not have the disease, the probability that the test gives a negative response is .90, or that the false positive rate of the test is .10. In the population, 1% of the people have the disease. What is the probability that a person tested has the disease, given the results of the test is positive? Let D e the event "the person has the disease" and let T be the event "the test gives a positive result."

All I really need to know is how to find $\displaystyle P(D)$. The rest I can handle on my own.

Thanks.

The way I solved it was this:

I need to find $\displaystyle P(D|T) = \frac{P(T|D)P(D)}{P(T|D)P(D) + P(T|D')P(D')}$

$\displaystyle P(D|T) = \frac{(0.95)(0.01)}{(0.95)(0.01) + (0.10)(0.99)}$

$\displaystyle P(D|T) = \frac{0.0095}{0.0095 + 0.099}$

$\displaystyle P(D|T) = \frac{0.0095}{0.1085}$

$\displaystyle P(D|T) = 0.0875$

Is that right?