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

. The rest I can handle on my own.

Thanks.

The way I solved it was this:

I need to find

Is that right?