A company is considering producing a new product. Based on past records, management believes that there is a 70 percent chance that the new product will be successful, and a 30 percent chance it will not be successful. Market research may be used to revise these probabilities. In the past, given the product was succesful, 90 percent of the time the market research was used. However, of the products that were not successful, 20 percent of the time market research was used.
What is the probability that the product is successful and market research was performed?