A company is introducing a new product. Historically, the co…
A company is introducing a new product. Historically, the company’s products are a success 60% of the time and a failure 40% of the time. Therefore, the prior probability of success is 0.6, and the prior probability of failure is 0.4. The company hires an analyst to predict whether the product will be a success. The analyst’s accuracy in predicting the performance of the product is 80%. (In other words, a product that succeeds will be predicted to be successful 80% of the time and a failure 20% of the time.) Given that the analyst predicts the product to be successful, what is the probability that the product will be a success? Provide your answer as a decimal number rounded to three decimal places.