(May, 1986) A company is considering the introduction of a new product

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(May, 1986) A company is considering the introduction of a new product. The marketing vice president believes that the probability of success for the product is .5. It will either be a complete success or a complete failure. The product will be test marketed regionally before being introduced nationally. In the past, the test market has been 75% reliable in making favorable predictions - that is, if a product is destined to be successful nationally, the test market will produce favorable results 75% of the time. The test market however has been 70% reliable in making an unfavorable prediction. That is, a product destined to be a failure nationally will produce an unfavorable result 70% of the time.

If the product is successfully nationally, the net profit will be $30,000,000. If it fails, the net loss will be $10,000,000.

If the test market indicates a favorable result, what is the expected net profit?