3 Emma has won a holiday worth $\pounds 1000$. She is wondering whether or not to take out an insurance policy which will pay out $\pounds 1000$ if she should fall ill and be unable to go on the holiday. The insurance company tells her that this happens to 1 in 200 people. The insurance policy costs $\pounds 10$. Thus Emma's monetary value if she buys the insurance and does not fall ill is $\pounds 990$.\\
(i) Draw a decision tree for Emma's problem. Use the EMV criterion in your calculations.\\
(ii) Interpret your tree and say what the maximum cost of the insurance would have to be for Emma to consider buying it if she uses the EMV criterion.

Suppose that Emma's utility function is given by utility $= \sqrt [ 3 ] { \text { monetary value } }$.\\
(iii) Using expected utility as the criterion, should Emma purchase the insurance?

Under this criterion what is the cost at which she will be indifferent to buying or not buying it?

Emma could pay for a blood pressure check to help her to make her decision. Statistics show that $75 \%$ of checks are positive, and that when a check is positive the chance of missing a holiday through ill heath is 0.001 . However, when a check is negative the chance of cancellation through ill health is 0.017.\\
(iv) Draw a decision tree to help Emma decide whether or not to pay for the check. Use EMV, not expected utility, in your calculations and assume that the insurance policy costs $\pounds 10$.

What is the maximum amount that she should pay for the blood pressure check?

\hfill \mbox{\textit{OCR MEI D2 2006 Q3 [20]}}