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April 19th, 2011, 10:24 PM  #1 
Newbie Joined: Apr 2011 Posts: 3 Thanks: 0  Request for Probality Problem Solution
Hi!! I request to kindly provide the solution of probability problem mentioned below. Though I feel that it can be solved by using Bayes theorem, but in case of second probability set the sum is more than 1. It would be great to have a complete solution rather than hint. With Kind Regards, Dwijendra Problem: A restaurant is experiencing discontentment among its customers. It analyses that there are three factors responsible viz. food quality, service quality and interior décor. By conducting an analysis, it assesses the probabilities of discontentment with the three factors as 0.40, 0.35 and 0.25 respectively. By conducting a survey among the customers, it also evaluated the probabilities of a customer going away discontented on account of these factors as 0.6, 0.8 and 0.5, respectively. With this information, the restaurant wants to know that, if a customer is discontented, what are the probabilities that it is so due to food, service or interior décor? 
April 20th, 2011, 02:20 PM  #2  
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 407  Re: Request for Probality Problem Solution Hello, Dwijendra! You're right . . . We need Bayes' Theorem. Quote:
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April 20th, 2011, 02:37 PM  #3 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,155 Thanks: 466 Math Focus: Calculus/ODEs  Re: Request for Probality Problem Solution
Great job, soroban! I found this question in numerous places online, but yours is the clearest explanation (not surprisingly)! Aside from the exact values you have given, the best I found were approximations and their expressions were extremely convoluted compared to yours! 

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A restaurant is experiencing discontentment among its customers. It analyses that there are three factors responsible viz. food quality, service quality and interior dÃ©cor. By conducting an analysis, it assesses the probabilities of discontentment with t,Math probality
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