### 8.3 Expected Value

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• Math Help

To make a spreadsheet similar to the one in Example 6(a), use the steps below.

1. Enter the titles "Result," "Payoff," "Probability," and "Expected Value" into row 1.
2. In column A under the title "Result," enter the titles "Complete loss," "No gain," "100% gain," "400% gain," "900% gain," and "Total."
3. In column B under the title "Payoff," enter the values -1000, 0, 1000, 4000, and 9000.
4. In column C under the title "Probability," enter the values 0.40, 0.15, 0.15, 0.15, and 0.15.
5. Enter the formula = B2*C2 into cell D2.
6. Select cell D2. From the Edit menu, choose Copy.
7. Select cells D3 through D6. From the Edit menu, choose Paste.
8. Enter the formula =SUM(C2:C6) into cell C7.
9. Enter the formula =SUM(D2:D6) into cell D7.

To format the cells, use the steps below.

1. Select cells B2 through B6.
2. From the Format menu, choose Cells....
3. In the Format Cells dialog, select the Number tab.
4. From the Category: list, select Currency.
5. For Decimal places:, enter 0. For Symbol, choose \$ from the drop down list. Then click OK.
6. Repeat steps 1-5 for cells D2 through D7.
7. Select cells C2 through C7.
8. From the Format menu, choose Cells....
9. In the Format Cells dialog, select the Number tab.
10. From the Category: list, select Percentage.
11. For Decimal places:, enter 0. Then click OK.
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• Checkpoint Solution

Assume that you invest \$1000. A spreadsheet showing the expected value of each investment is shown below.

If you have to pick only one investment, I think that the conservative investment is the best choice because it has only a slight chance of loss and is still expected to have a decent return. The expected value of the payoff is \$105. This is a return of

On the other hand, if you could make a great number of speculative investments, the average payoff would approach the expected value, \$1350. This is a very high return of

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