\problemdata                                                             
        {A posteriori probability} % latex-friendly label for the prob.
        {conditional probability} % The topic(s) of the problem content.  
        {`A first course in Probability" p 124, exercise 8} % Source (if known)                                          
        {S01 Final, 10} % Usage (list ones you are aware of). 
        {Tina Wang, S02} % Last revision info (author, date).   
                                                                         
                                                                         
\begin{problem}       
\begin{problemparts}    
You ask your neighbor to water a sickly plant while you are on
vacation. Without water, it will die with probability $0.8$; with
water it will die with probability $0.15$. You assume a 90\%
probability that your neighbor will remember to water the plant.

\problempart What is the probability that the plant will be alive when you return?
\solution{
0.785}


\problempart If it is dead, what is the probability that your neighbor forgot to water it?
\solution{
\[
\frac{16}{43}=0.372
\]
}
\end{problemparts}
\end{problem}
                                 