Probability of Success of Happy Harrys Hamburgers

Question

Happy Harry's Hamburgers recently commissioned a top tier consulting company to develop a new location selection process. However, after receiving the first invoice from the consulting company, Happy Harry wasn't... happy that is, and he decided to cancel the remainder of the engagement.

Along with the invoice, the consulting company provided Happy Harry with the results of their study to date. The company had analyzed Happy Harry's previous location selections, categorizing them as huge successes, successes, or failures. Here is what they reported:

77.19 % of past locations were a success 
17 % of past locations were a failure

Happy Harry was underwhelmed by this information. However, the company also applied a model it developed to Harry's past hugely successful, successful, and failed locations. Given a huge success, the model predicted success 93.5 % of the time. Given a success, the model predicted success 92.5 % of the time. Given a failure, the model predicted failure 77.5 % of the time.

Now what Happy Harry really wants to know is the probability of a success given a predicted success. So, give Harry a helping hand and calculate Pr{S|PS}:

Hint: To answer this problem, you will want to use your knowledge of complementary probabilities, conditional probabilities, Bayes' Theorem, and the law of total probabilities.

 Thus the P(S|PS) = 0.3944

Summary

This question belongs to statistics and discusses about calculating the probability of a success.

Word count: NA