Thread: question on probability and bayes

1. question on probability and bayes

Let A be the event that a patient has cancer. In the course of a hospital stay,
the doctors on duty learn the results of test T1. A little later they learn the results of
test T2. Is it possible that, considered separately, positive results on T1 and T2 might
each increase the chance of A (i.e., P(A|T1) > P(A), and P(A|T2) > P(A)), but that if
both are known to be positive they decrease the chance of A (i.e., P(A|T1; T2) < P(A))?
Explain your answer either with a clear example or in the style of a mathematical
demonstration.

Any help? Having trouble understanding the question...

2. Re: question on probability and bayes

Originally Posted by amma0913
Let A be the event that a patient has cancer. In the course of a hospital stay,
the doctors on duty learn the results of test T1. A little later they learn the results of
test T2. Is it possible that, considered separately, positive results on T1 and T2 might
each increase the chance of A (i.e., P(A|T1) > P(A), and P(A|T2) > P(A)), but that if
both are known to be positive they decrease the chance of A (i.e., P(A|T1; T2) < P(A))?
Explain your answer either with a clear example or in the style of a mathematical
demonstration.

Question: Do we know if the events $T_1~\&~T_2$ independent or not?

3. Re: question on probability and bayes

Yes, they're independent.