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Problem 1: A government committee is considering the economic benefits of a program of preventative flu vaccinations.

Problem 1:

A government committee is considering the economic benefits of a program of preventative flu vaccinations. We will assume that the flu vaccine is completely effective so if the vaccine is implemented, there will be no flu cases. It is estimated that a vaccination program will cost $7 million and that the probability of flu striking in the next year is 0.75. If vaccinations are not introduced then the estimated cost to the government if flu strikes in the next year is $7 million with probability 0.1, $10 million with probability 0.3 and $15 million with probability 0.6.


One alternative open to the committee is to institute an "early-warning" monitoring scheme (costing$3 million) which will enable it to detect an outbreak of flu early. If the scheme detects a flu early, then the committee must decide whether or not to institute a rush vaccination program (costing $10 million because of the need to vaccinate quickly before the outbreak spreads, again with the vaccine being completely effective) or to do nothing with the costs and probabilities listed previously for a flu strike.


a) Draw decision tree for this scenario, making sure you label all branches and include all probabilities and consequences.


b)Solve the decision tree using EMV and state what recommendations should the committee make to the government.




Problem 2:


You go to the racetrack and are choosing between 2 horses: Belle and Jeb (you are at the racetrack, so you will bet on one of these two horses). Betting on either horse will cost you $1, and the payoffs are as follows:


•Bet on Belle: you will be paid $2 if she wins (or a net profit of $1). You believe she has a 70%chance of winning.

•Bet on Jeb: you will be paid $11 if he wins (for a net profit of $10). You believe that he has a10% chance of winning.


Prior to making your decision of which horse to bet on, someone comes and offers you gambler's insurance. If you agree to the gamblers insurance, they pay you $2 immediately and you agree to pay them 50% of the winning (that is, $0.50 if Belle wins, $5 if Jeb wins, and 0 otherwise).

What should you do?


Answer this question by:


a)Creating a decision tree for this scenario, making sure you label all branches and include all probabilities and consequences.



b)Solving the decision tree using EMV and stating the optimal decision strategy.

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