Mark Martinko has been a class A racquetball payer for the past five years, and one of his biggest goals is to own and operate a racquetball facility. Unfortunately, Market thinks that the change of a successful racquetball facility is only 30%. Mark's lawyer has recommended that he employ one of the local marketing research groups to conduct a survey concerning the success or failure of a racquetball facility. There is a 0.8 probability that the research will be favorable given a successful racquetball facility. In addition, there is a 0.7 probability that the research will be unfavorable given an unsuccessful facility. Compute revised probabilities of a successful racquetball facility given a favorable and given an unfavorable survey.
Let S=Successful racquetball facility
F= Unsuccessful racquetball facility
Given P(S)=0.30 P(P/S)=0.80 and P(U/F)=0.7
We know that ...
This post explains how to calculate the probability of success or failure given the survey outcome. The illustrates the use of Bayes theorem and conditional probabilities to calculate the post-hoc probabilities.