1. (Easy) Among all victims of zombie bites, $10 \%$ are prescribed the experimental drug Undetenin to treat them. Overall, $4 \%$ of the human population suffer an adverse reaction to Undetenin. Out of all the patients being treated with Undetenin, $2 \%$ suffer an adverse reaction to the drug. What is the probability that a patient allergic to Undetenin is prescribed the drug?
Answer: $5 \%$
Solution: This is an application of Bayes' theorem. If $A$ is the event of being prescribed Undetenin and $B$ is being allergic to it, then we are looking for $P(A \mid B)$. We have $P(A \mid B)=\frac{P(B \mid A) P(A)}{P(B)}=$ $\frac{(0.02)(0.1)}{0.04}=0.05$.