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.
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
The solution calculates the expected value of information.