I assume you want P(Disease|Positive)=P(D|P)=P(DP)/P(P)
NOW P(DP)=P(P|D)P(D)
and P(D)=P(PD)+P(PD')=P(P|D)P(D)+P(P|D')P(D')
A dreaded new disease is sweeping the nation. Its called the Bucolic Plague.
A test has been developed that can detect whether you have the disease- the test is 99% ACCURATE. That is if you don't have the disease, that is there will be a 99% chance the test will detect it. If you don't have the disease, the test will be 99% accurate saying you don't.
In the general population, 0.1 percent of people have the disease- thats one-tenth of a percent.
You decide to get the test. you get you resultositive. Now what?
What is the probability you have the disease?
Needs a Tree diagram to lay it out.
what is the sample space?
probabilities for assigned calculations.
probability distribution function
written summary.
word processing report.
We can't answer the question since we are told nothing about the accuracy of the test when the subject has the disease. The probability of the subject having the disease given a postiive test result depends also on the probability of a false positive.