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# Numerical example utilizing principles of probability theory

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A gardener can use one of the three brands of fertilizers during the next growing season. The following decision table attached shows the expected gross income per acre for each fertilizer brand and weather condition for the growing season. The chance of dry season is shown by probability P. Find the range of P values where Brand-B fertilizer has the highest expected returns compared to using the two alternative fertilizer brands.

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#### Solution Preview

Season
Dry Wet
P 1 - P
Fertilizers Brand-A 110 60
Brand-B 100 140
Brand-C 80 160

Expected Returns from using Brand A = 110 * P + 60 * (1-P) = 110P + 60 - 60P = 50P + ...

#### Solution Summary

The example shows the computation of expected return by utilizing the principles of probability theory

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