Question

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?

Answer 1

Answer: Our required probability is 0.7273.

Step-by-step explanation:

Since we have given that

                                Actually successful   Actually failure   Total

Predicted successful                0.4                  0.15            0.55

Predicted failure                        0.1                  0.35             0.45

Total                                           0.5                  0.50                 1

Probability that the market research firm would predict that it would be success.

P(Actual success|Predicted success) is given by

$\dfrac{0.4}{0.55}=0.7273$

Hence, our required probability is 0.7273.