A lawyer believes that the probability is .3 that she can win a discrimination suit. If she wins the case, she will make $400,000; but if she loses, she gets nothing. Assume that she has to spend $75,000 preparing the case. What is her expected gain

her expected gain is $45,000.

Explanation:

If she wins

She will make = $400,000

Probability of winning = 0.3

Expected income = $400,000 x 0.3 = $120,000

Cost on the cash = $75,000

Expected gain = Expected income - Cost  = $120,000 - $75,000 = $45,000

If she loses the case she has to bear the cost incurred to prepare the case. So, the probability on the cost side is 1 but probability on the income side is 0.3 so we calculated the 0.3 probable income which is $120,000 after deducting the cost the lawyer will have expected gain of $45,000 only.

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