# Tree Diagram with backwards induction analysis and posterior probability

**Question description**

The facts: young producer has just completed a movie that turned out better than expected. The producer was going to sell the movie to cablevision, but now also wants to consider selling to movie theaters. The producer is considering hiring a theatrical consulting firm to test show the movie overseas and to tabulate the responses of movie buffs. The result will either be: Extremely Positive (EP), Positive but Reserved (PR), or a negative reaction (NR). Ultimatley the movie will be a success (S) or failure (F).

The producer believes the film if it is a success and sold to cablevision, will net $12million and net $2million if it's a failure. If it is sold to the theater and it is a success, the net is $25million, but a failure would result in a $5million dollar loss. The survey, if performed overseas, will cost $2million.

The producer believes that the following probabilities may apply: Pr(S) =.3, PR(EP/S) =.7, Pr(PR/S) = .2, Pr(NR/F) =.8, and Pr(PR/F) = .1. Determine the appropriate posterior probabilities [Pr(S|EP), Pr(F|EP), Pr(S|PR), Pr(S|NR), and Pr(F|NR)] and perform a backwards induction analysis to determine if the experimental information should be obtained.

*Note: I am supposed to change 1 variable from the above problem. I chose to write it out exactly as is so that I could better understand where this variable is being changed. The variable I am to change is: Probability of Success... so omit what is provided for Probability of Success in the original stated question above and use .22 instead.

I have 2 more problems such as this, and if I could get a push start that would be much appreciated.

Thank you!

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