I attempted the question and used bayes theorem and got the same answer as what you got.
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.
The way I solved it was this:
I need to find
Is that right?
The reason why I posted this was because I multiplied 0.10 and 0.99 wrong and couldn't arrive at the correct answer. But I do have one more question, the answer in my book provides this:
But, what is P(T) without knowing whether or not the person has the disease? Or are you supposed to assume that they have the disease? I tried both scenarios and couldn't arrive at that solution.