document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=935071>Question 935071</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi,<BR>\n" );
document.write( "I have the following question which I have worked on but want to ensure I have the answers correct, if someone could do this it would be great. \r<BR>\n" );
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document.write( "International Pictures is trying to decide how to distribute its new movie 'Claws'. 'Claws' is the story of an animal husbandry experiment at the University of Southern Queensland that goes astray, with tragic results. An effort to breed meatier chickens somehow produces an intelligent, 200 kilogram chicken that escapes from the lab and terrorises the campus. In a surprise ending the chicken is befriended by coach Tim Galvano, who teaches it how to play Rugby and help his team win State, National and World Championships. Because of the movie's controversial nature, it has the potential to be either a smash hit, a modest success, or a total bomb. International is trying to decide whether to release the picture for general distribution initially or to start out with a 'limited first-run release' at a few selected theatres, followed by general distribution after 3 months. The company has estimated the following probabilities and conditional profits for 'Claws':									<BR>\n" );
document.write( "profits(millions$)								level of success, probability, limited release, general distribution<BR>\n" );
document.write( "Smash, 0.3, 22, 12<BR>\n" );
document.write( "Modest, 0.4, 9, 8<BR>\n" );
document.write( "Bomb, 0.3,-10, -2<BR>\n" );
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document.write( "International can run sneak previews of 'Claws' to get a better idea of the movies' ultimate level of success. Preview audiences rate movies as either good or excellent. On the basis of past experiences, it was found that 90% of all smash successes were rated excellent (and 10% rated good), 75% of all modest successes were rated excellent (25% rated good) and 40% of all bombs were rated excellent (60% rated good). The cost of running sneak previews is not cheap. Currently, this stands at $1m.									\r<BR>\n" );
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document.write( "1/What is the opportunity loss for a General Distribution for a Smash level of success?<BR>\n" );
document.write( "$10m, calculated figures into an opportunity loss table which gave me the following results<BR>\n" );
document.write( "level of success, limited release, general distribution<BR>\n" );
document.write( "Smash, 0, 10<BR>\n" );
document.write( "Modest, 0, 1<BR>\n" );
document.write( "Bomb, 8, 0\r<BR>\n" );
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document.write( "2/What would the optimal action be for International before running the sneak preview?<BR>\n" );
document.write( "a/Run a limited release with an expected payoff of $7.20m<BR>\n" );
document.write( "b/Run a limited release with an expected payoff of $6.20m<BR>\n" );
document.write( "c/Run a general release with an expected payoff of $7.20m<BR>\n" );
document.write( "d/Run a general release with an expected payoff of $6.2m<BR>\n" );
document.write( "I chose A, putting the choices and parameters into a decision tree I got 7.2 for limited release and 6.2 for general release and chose limited due to best return\r<BR>\n" );
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document.write( "3/What is the maximum amount of money that International would be prepared to pay for an absolutely reliable forecast of the movies’ level of success?<BR>\n" );
document.write( "a/$9.6m<BR>\n" );
document.write( "b/$7.2m<BR>\n" );
document.write( "c/$6.2m<BR>\n" );
document.write( "d/$2.4m<BR>\n" );
document.write( "I chose B, adding onto the original data I chose the best profit for each level and assigned the probability to each of these and summed them up.  Smash, 22 prof x 0.3 prob + modest 9 prof x 0.4 prob + bomb -2 prof x 0.3 prob which gave me 9.6.\r<BR>\n" );
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document.write( "4/What would be the joint probability for a ‘smash success’ and good preview given that in the past, it was found that 10% of all smash successes were rated good?<BR>\n" );
document.write( "0.03, this is the 0.3 probability for a smash x 10% good rating for a smash\r<BR>\n" );
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document.write( "5/What is the posterior probability of a bomb given the sneak preview indicates excellent?<BR>\n" );
document.write( "0.1739, this was worked out in a table which in part was the following info, 0.3 bomb x 0.4 estimate excellent/bomb = 0.12.  Used the total for excellent estimates 0.69, divided 0.12 / 0.69 = 0.1739.\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #568430 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=568430\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> following probabilities and conditional profitsfor ‘Claws’:<BR>\n" );
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document.write( "		PROFITS (Millions of $)\r<BR>\n" );
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document.write( "Level of success-------	Probability-------	Limited release-------		General distribution\r<BR>\n" );
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document.write( "Smash---------------------	.3--------------------- 22---------------------	12\r<BR>\n" );
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document.write( "Modest---------------------	.4--------------------- 9--------------------- 8\r<BR>\n" );
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document.write( "Bomb--------------------- .3	---------------------	    –10--------------	-------		  –2\r<BR>\n" );
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document.write( "If International Pictures' past experiences can be used as proxies for probabilities related to the current film \"Claws,\" then let<BR>\n" );
document.write( "P(S) = 0.3 be the probability that the film is a smash hit,<BR>\n" );
document.write( "P(M) = 0.4 be the probability that the film is a modest success,<BR>\n" );
document.write( "P(B) = 0.3 be the probability that the film is a total bomb,<BR>\n" );
document.write( "P(E | S) = 0.90 be the probability of an excellent preview, given the film is a smash hit,<BR>\n" );
document.write( "P(E | M) = 0.75 be the probability of an excellent preview, given the film is a modest success, and<BR>\n" );
document.write( "P(E | B) = 0.40 be the probability of an excellent preview, given the film is a total bomb.\r<BR>\n" );
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document.write( "The posterior probability of a modest success given the sneak preview indicates excellent now can be written as<BR>\n" );
document.write( "P(M | E) = P(M & E) / P(E)<BR>\n" );
document.write( "= P(M)P(E | M) / [P(S)P(E | S) + P(M)P(E | M) + P(B)P(E | B)]<BR>\n" );
document.write( "= (0.4)(0.75) / [(0.3)(0.9) + (0.4)(0.75) + (0.3)(0.4)]<BR>\n" );
document.write( "= 0.30 / [0.27 + 0.30 + 0.12]<BR>\n" );
document.write( "= 0.30 / 0.69<BR>\n" );
document.write( "= 10 / 23<BR>\n" );
document.write( "= 0.43 (to two decimal places).\r<BR>\n" );
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