Question

A lawyer believes that the probability is .3 that she can win a discrimination suit. if she wins the case she will make $40,000, but if she loses she gets nothing. assume that she has to spend $5000 preparing the case. what is her expected gain?

Answer 1

The net expected gain is $7,000.

Further Explanation:

Probability:

Probability refers to the possibility of the occurrence of any event. The probability can be expressed between 1 to 0. The 0 probability states that there are no chances that a specific event will occur. The 1 probability states that the event will defiantly occur. Probability is calculated by dividing the favorable cases with the total number of cases.

Expected gain at the time of winning the case:

The probability of winning the case is 0.30. At the time of winning the case, the lawyer will get $40,000.  However, she will incur $5,000 for the preparation of the case. Therefore, the net winning of the lawyer will be $35,000 ($40,000 - $5,000). The probability of winning the case can be calculated as follows:

$\begin{aligned}\text{Expected gain (Winning)}&=\text{Net winning}\times{\text{Winning probability}}\\&=\ 35,000\times{0.30}\\&=\ 10,500\end{aligned}$

Expected loss at the time of losing the case:

The probability of losing the case is 0.70 (1-0.30). At the time of losing the case, the lawyer will incur $5,000 which the cost of the preparation of the case. Therefore, the net loss at the time of losing the case is $5,000.

$\begin{aligned}\text{Expected gain (Losing)}&=\text{Net loss}\times{\text{Losing probability}}\\&=(\ 5,000)\times{0.70}\\&=(\ 3,500)\end{aligned}$

Net expected gain:

$\begin{aligned}\text{Net Expected gain}&=\text{Expected gain (Winning)}+\text{Expected gain (losing)}\\&=\ 10,500+(\ 3,500)\\&=\ 7,000\end{aligned}$

Thus, the net expected gain is $7,000.

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Answer Details:

Grade: Senior school

Chapter: Probability  

Subject: Statistics  

Keywords: lawyer, believes, probability, she, win, discrimination, suit, wins, case, will make, loses, assume, she, spend, preparing, expected gain.

Answer 2

Her expected gain is $7,000 based on the information shown on the question above. This problem can be solved by using the expected value formula which stated as EV = W*Pw-L*Pw where EV is the expected value, W is the win value, Pw is the probability of winning, L is the lost value and Pl is the probability of losing. Calculation: 7,000 = (40,000-5,000)*0.3 - 5,000*(1-0.3)