To improve her decision-making capability, the electronics products manufacturer in Exercise 22.16 performs a survey of potential buyers of compact disc players. She describes the product to 25 individuals, 3 of whom say they would buy it. Using this additional information together with the prior probabilities, determine whether the new product should be produced.

In exercise 22.16

An international manufacturer of electronic products is contemplating introducing a new type of compact disk player. After some analysis of the market, the president of the company concludes that, within 2 years, the new product will have a market share of 5%, 10%, or 15%. She assesses the probabilities of these events as .15, .45, and .40, respectively. The vice-president of finance informs her that, if the product captures only a 5% market share, the company will lose $28 million. A 10% market share will produce a $2 million profit, and a 15% market share will produce an $8 million profit.