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Math Word Problem

When there is not enough rain, Friendly Farms needs to supplement with irrigation. The profit when there is sufficient rain during the maximum growth period is $4000 per acre. If it does not rain during this period, the profit is only $1600 per acre. Using this information, what profit per acre, on average, can Friendly Farms expect to make? What math strategy do I use to solve this problem?

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First, you need to get the probability of the two events - not enough rain and enough rain.
The probability of not enough rain is 1 less the probability of enough rain.

Supposing that the probability of not enough rain is 0.70, then the probability of enough rain is 0.30.

Therefore to get the profit per acre, you multiply these probabilities with their profits per acre. Hence,
$4000 * 0.30 + $1600 * 0.70 = $2,320 is the average profit per acre.

The above method uses the mathematics principle of the weighted expected returns.

I hope this helps.

Posted on May 10, 2009

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