My Math Forum Request for Probality Problem Solution

 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:
 A restaurant is experiencing discontentment among its customers. It analyses that there are three factors responsible: 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 [color=beige]. . [/color]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 (a) food, (b) service or (c) interior décor?

$\text{Let }D\text{ represent the customer's Discontent.}$

$\text{We are given these facts:}$

[color=beige]. . [/color]$\begin{arra}{c|c|c|} & \text{Cause} & \text{D} \\ \\ \\ \hline \text{food} & 0.40 & 0.6 \\ \text{service} & 0.35 & 0.8 \\ \text{decor} & 0.25 & 0.5 \\ \\ \\ \hline \end{array}$

$\text{W\!e have: }\;\begin{Bmatrix}P(\text{food}\,\wedge\,\text{D})=&(0.40)(0.6)=&0.240 \\ \\ \\ P(\text{srvc}\,\wedge\,\text{D})=&(0.35)(0.8)=&0.280 \\ \\ \\ P(\text{decor}\,\wedge\,\text{D})=&(0.25)(0.5)=&0.125 \end{Bmatrix}=$

$\text{Hence: }\:P(D) \:=\:0.240\,+\,0.280\,+\,.125 \:=\:0.645$

$(a)\;P(\text{food}\,|\,\text{D}) \;=\;\frac{P(\text{food}\,\wedge\,\text{D})}{P(D)} \;=\; \frac{0240}{0.645} \;=\;\frac{48}{129}$

$(b)\;P(\text{srvc}\,|\,\text{D}) \;=\; \frac{P(\text{srvc}\,\wedge\,\text{D})}{P(D)} \;=\;\frac{0.280}{0.645} \;=\;\frac{56}{129}$

$(c)\;P(\text{decor}\,|\,\text{D}) \;=\;\frac{P(\text{decor}\,\wedge\,\text{D})}{P(D) } \;=\;\frac{0.125}{0.645} \;=\;\frac{25}{129}$

 April 20th, 2011, 02:37 PM #3 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,204 Thanks: 511 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!

 Tags probality, problem, request, solution

,

### Math probality

Click on a term to search for related topics.
 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post PerMortenIvar Algebra 1 February 16th, 2012 02:16 PM Isbell New Users 7 February 8th, 2012 07:39 PM TreeTruffle Algebra 2 March 27th, 2010 01:22 AM bigli New Users 2 December 31st, 2006 07:41 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top