3-41 Peter Martin is going to help his brother who wants to open a food store. Peter initially believes that there is a 50-50 chance that his brother's food store would be a success. Peter is considering doing a market research study. Based on historical data, there is a 0.8 probability that the marketing research will be favorable given a successful food store. Moreover, there is a 0.7 probability that the marketing research will be unfavorable given an unsuccessful food store.

If the marketing research is favorable, what is Peter's revised probability of a successful food store for his brother?

If the marketing research is unfavorable, what is Peter's revised probability of a successful food store for his brother?

If the initial probability of a successful food store is 0.60 (instead of 0.50), find the probabilities in parts (a) and (b).