## [solution]: Use the following diagram of the widget market in a small country

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Probability &amp; Statistics for Business and

Economics Bonus Problem

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

Dick Roper to read the script and

assess its chances of success. Roper is generally able to

correctly predict a successful film 70% of the time and

correctly predict an unsuccessful film 80% of the time. Roper

wants a fee of \$1 million.

Success

Produce Film

Don?t Produce Film

Flop

EMVs

\$25M

\$0

-\$8M

\$0

-\$4.7M

\$0

1. (8 points) Determine the revised (posterior) probability for each state of nature

(round at 2 decimals)

2. (8 points) Determine the strategy Mogul should follow if Roper is hired ( i.e.

recalculate EMVs based on good review and bad review).

3. (4 points) Determine the expected value of the strategy.

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