A market research firms 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).For any randomly selected new product, what is the probability that the market research firm would predict that it would be a success?

Question

Quizplus · Accepted Answer

The probability that a product is predicted to be a success is the sum of the probabilities of two events: (1) the product is actually successful and predicted as such, and (2) the product is actually a failure but is incorrectly predicted to be a success. This can be calculated as (0.5 * 0.8) + (0.5 * 0.3) = 0.4 + 0.15 = 0.55.

A Market Research Firms Conducts Studies Regarding the Success of New