In context, $A$ refers to the event of getting a positive in a cancer test and $B$ is the event of actually having cancer. i.e. Prove: True positive rate $\geq$positive rate $\geq$false positive rate
question b: Prove: For a test in which the false positive rate is $1$ in $n$, the posterior probability of $B$ given a positive test is at most a factor of $n$ times larger than the prior probability (incidence) of $A$.
question c: Given $P(B)\sim 0$ and $P(A|B)\sim 1$ prove $P(B|A)\sim P(B)/P(A/B')$ Note: $B'$ is complement of $B$.