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(i) Explain the concept of opportunity loss, and show that the minimum opportunity loss is equal to the Expected Value of Perfect Information.

(ii) The failure rate in a particular examination is estimated to be $40 \%$. Construct a table showing the probabilities of $0,1,2 \ldots 5$ students failing in a sample of five.

(iii) 150 graduate entrants are due to take their first professional accounting exam at the Institute of Certifiable Accountants. The probability distribution for the failure rate is estimated in the following table:

$\begin{array}{ll}\text { Failure rate } & \text { Probability } \\ 0.1 & 0.1 \\ 0.2 & 0.2 \\ 0.3 & 0.3 \\ 0.4 & 0.3 \\ 0.5 & 0.1\end{array}$

Each failing student is entitled to a $&pound; 10$ refund on professional fees. The Institute's senior tutor is confident that she could ensure a failure rate of $0.1$ by holding an intensive revision course, at a cost to the Institute of $&pound; 300$. Advise the Institute on whether the revision course should take place.

A tutorial test of five students resulted in no failures. Use this information to revise the failure rate probability distribution, and hence reassess the revision course.
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