hi experts in probability, i really need help in following probability question. i got stucked here. the question goes like this: 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). If the market research predicted that the product would be a success, what is the probability that it actually would be a success? pleae help me. i would really appreciate your help. thank you.