I ran into this question in my class and am not sure how to solve it:
A positive test result gives you a Bayes factor of 71 in favor of being sick. If your prior probability of Being sick was 0.05, what is your posterior probability of being sick.
I understand that a Bayes factor is basically the likelihood ratio and I know that $p(M_2)=.01$. I guess I am looking for $p(M2|y=\text{testing positive for sick})$, but I am missing all the other variables.
Can someone please give me a hint how to proceed?
self-study
to your tags as it will avoid answers that provide a complete resolution of this problem, without letting you gain by solving the final step. $\endgroup$