Assignment:
Market Researchers, Inc. has been hired to perform a study to determine if the market for a new product will be good or poor. In similar studies performed in the past, whenever the market actually was good, the market research study indicated that it would be good for 85% of the time. On the other hand, whenever the market actually was poor, the market study incorrectly predicted it would be good 20% of the time. Before the study is performed, it is believed there is a 70% chance the market will be good. When Market Researchers, Inc. performs the study for this product, the results predict the market will be good. Given the results of the study, what is the probability that the market will be good?
Provide complete and step by step solution for the question and show calculations and use formulas.