A market research firm conducts studies regarding the success of new products. The company is not always perfect in predicting the success. Suppose that there is a 50% chance that any new product would be successful (and a 50% chance that it would fail). In the past, for all new products that ultimately were successful, 80% were predicted to be successful (and the other 20% were inaccurately predicted to be failures). Also, for all new products that were ultimately failures, 70% were predicted to be failures (and the other 30% were inaccurately predicted to be successes). If the market research predicted that the product would be a success, what is the probability that it would actually be a success?
a)0.27
b)0.73
c)0.80
d)0.24
e)1.00