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Expected value of information

Jeffrey Mogul is a Hollywood film producer and he is currently evaluating a script by new screenwriter and director, Betty Jo Thurston. Jeffrey knows that the probability of a film by a new director being a success is about .10 and the probability it will flop is .90. The studio accounting department estimates that if this film is a hit, it will make $25 million in profit, whereas if it is a box office failure, it will lose $8 million. Jeffrey would like to hire noted film critic Gene Sickel to read the script and assess its chances of success. Sickel is generally able to correctly predict a successful film 70% of the time and correctly predict an unsuccessful film 80% of the time. Sickel wants a fee of $1 million. Determine if Sickel should be hired, the strategy Mogul should follow if Sicket is hired, and the expected value. Please show all work and provide explanation.

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Let us calculate the probability that a film would be a success after Sickel has predicted that it would be a success

Let us say there are 100 films
0.1 of these films ,i.e. 10 are success and
0.9 of these films ,i.e. 90 are failures

Sickel predicts a successful film 70% of the time
Thus 7 of the would be 10 successful films would be predicted to be successful
and 3 of the would be 10 successful films would be predicted to be failures

Sickel ...

Solution Summary

The solution calculates the expected value of information.