# CollGraduate Statistics: Tree Diagram, Probability, Backward Induction Analysis

*label*Statistics

*timer*Asked: Apr 5th, 2015

**Question description**

Hello- Please, oh please can someone help me as soon as possible? I have been at this for almost 72 hours and I am getting no where. Something just isn't clicking for me. :/ This is time sensitive, due tomorrow- your assistance is more than very much appreciated!

** IMPORTANT NOTE for Questions 1 and 2**: I am supposed to change 1 variable from Question 1 and 2. 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 please omit what is provided for

**Probability of Success**in the original stated questions and use

**.22**instead.

**Question 1**

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

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.

**Question 2**

A decision must be made to go or not with a small merger. If we go through with it, the outcome will either be a Success (S) or a Failure (F). We are thinking a bout hiring a consultant to aid in the decision making process. The outcome witll either be favorable (F) or unfavorable (Unf.)

If no additional information is obtained, a successful merger will net $200,000, but an unsuccessful one will lose $75,000. The consulting firm, if utilized, will cost $10,000. The overall probability for a successful merger =.3. The appropriate conditional probabilities are Pr(Fav|S) = .8 and Pr(Fav|F) =.4. Determine the appropriate posterior probabilities and perform a backwards induction analysis to determine if the experimental information should be obtained.

**Question 3**

***IMPORTANT NOTE for Question 3: **I am supposed to change 1 variable from Question 3. 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 please omit what is provided for **Probability of Success** in the original stated question and use **.34** instead.

A rock group is making a comeback and think that they have a hot tune. However, it will hold it back if the public doesn't like it. It is thinking about trial testing it in several cities. The group believes that the trial test will either lead to super ratings (Sup), good ratings (Good), okay ratings (Ok), or poor ratings (Poor). Ultimately, the song will either be a success (S) or a failure (F).

If the record is a hit $20 million in profits will be generated. However, if it's not, the image will be tarnished and the group will lose $6 million from advertising. The trial testing will cost $0.5 million which is not included in the figures already given.

The group believes the probability of success is .4. The conditional probabilities are: Pr(Sup|S) =.4, Pr(Sup|F) = 1, Pr(Good|S) =.4, Pr(Good|F) = .2, Pr(Ok|S) =.1, Pr(Ok|F)=.3. Determine the appropriate posterior probabilities [Pr(S|Sup), Pr(F|Sup), Pr(S|Good), Pr(F|Good), Pr(S|Ok), Pr(F|Ok), Pr(S|Poor), and Pr(F|Poor)] and perform a backwards induction analysis to determine if the experimental information should be obtained.