8.3 Expected Value

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• Math Help

In Example 2(c), if the company sells 100,000 policies that have an annual premium of \$300, then the company can expect to gross

If the probability of a house fire is 0.0002, then the company can expect that the number of fires among the 100,000 policies will be

Because each policy is for \$200,000, the company can expect that the total amount of the payouts will be

This leaves a gross profit of

• Consumer Suggestion

There are lots of ways you can assist in preventing a fire in your home. One of the most important measures is to make sure you regularly check and change the batteries in the smoke alarms. Also, candles should never be left unattended and you should stay in the kitchen while preparing food. For more tips on fire safety and prevention, visit the U.S. Fire Administration.

• Checkpoint Solution

Some properties may not be completely insured. For instance, in Example 2, the policy pays \$200,000 if there is a house fire, but the value of the house could be more than \$200,000. Also, some properties may not be insured at all.

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