To calculate the expected value of the profit from the investment, we will multiply each outcome by its probability and then sum these values.
Let’s define the outcomes and their probabilities:
- Probability of a $22,000 loss: 0.38
- Probability of a $95,000 profit: 0.29
- Probability of a $42,000 profit: 0.15
- Probability of breaking even ($0 profit): 0.18
Now, we can calculate the expected value:
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For the loss of $22,000: \[ E(Loss) = 0.38 \times (-22000) = -8356 \]
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For the profit of $95,000: \[ E(Profit) = 0.29 \times 95000 = 27550 \]
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For the profit of $42,000: \[ E(Profit) = 0.15 \times 42000 = 6300 \]
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For breaking even ($0): \[ E(BreakEven) = 0.18 \times 0 = 0 \]
Now, we can sum these contributions to get the expected value of the profit: \[ E(Expected\ Value) = E(Loss) + E(Profit_{95000}) + E(Profit_{42000}) + E(BreakEven) \] \[ E(Expected\ Value) = -8356 + 27550 + 6300 + 0 \] \[ E(Expected\ Value) = -8356 + 27550 + 6300 = 27494 \]
Therefore, the expected value of the profit from the investment is $27,494.