2 Graham skis each year in an Italian resort which shares a ski area with a Swiss resort. He can buy an Italian lift pass, or an international lift pass which gives him access to Switzerland as well as to Italy. For his 6-day holiday the Italian pass costs $€ 200$ and the international pass costs $€ 250$. If he buys an Italian pass then he can still visit Switzerland by purchasing day supplements at $€ 30$ per day.

If the weather is good during his holiday, then Graham visits Switzerland three times. If the weather is moderate he goes twice. If poor he goes once. If the weather is windy then the lifts are closed, and he is not able to go at all.

In his years of skiing at the resort he has had good weather on $30 \%$ of his visits, moderate weather on $40 \%$, poor weather on $20 \%$ and windy weather on $10 \%$ of his visits.\\
(i) Draw a decision tree to help Graham decide whether to buy an Italian lift pass or an international lift pass. Give the action he should take to minimize the EMV of his costs.

When he arrives at the resort, and before he buys his lift pass, he finds that he has internet access to a local weather forecast, and to records of the past performance of the forecast. The 6-day forecast is limited to "good"/"not good", and the records show the actual weather proportions following those forecasts. It also shows that $60 \%$ of historical forecasts have been "good" and $40 \%$ "not good".

\begin{center}
\begin{tabular}{|l|l|l|l|l|l|}
\hline
\backslashbox{Forecast}{Actual} & good & moderate & poor & windy & proportion of forecasts \\
\hline
good & 0.4 & 0.5 & 0.1 & 0.0 & 0.6 \\
\hline
not good & 0.15 & 0.25 & 0.35 & 0.25 & 0.4 \\
\hline
\end{tabular}
\end{center}

(ii) Draw a decision tree to help Graham decide the worth of consulting the forecast before buying his lift pass. Give the actions he should take to minimize the EMV of his costs.

\hfill \mbox{\textit{OCR MEI D2 2013 Q2 [16]}}