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calculate the expected net profit

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Information I have gathered from the problem. I have a new product that has a probability .5 of being a success and probability .5 of being unsuccessful. Sucessful products pass quality control 80% of the time. Unsuccessful products pass quality control 25% of the time.

If the product is successful the net profit for the company would be $40 million; if unsuccessful the net loss would be $15 million. How do I calculate the expected net profit if the product passes quality control?

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This posting guides to calculate the expected net profit.

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We have the following assumptions.
A: A product is successful.
B: A product passes quality control.
~A means "Not A" and ~B means "Not B".
From the ...

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