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An insurance company knows that the average cost to build a home in a new California subdivision is ​$92 comma 297 and that in any particular year there is a 1 in 41 chance of a wildfire destroying all the homes in the subdivision. Based on these data and assuming the insurance company wants a positive expected value when it sells​ policies, what is the minimum the company must charge for fire insurance policies in this​ subdivision?

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Answer:

The minimum the company must charge for fire insurance policies in California​ subdivision is $2,252.

Explanation:

We have the chance of a wildfire destroying all the homes in the subdivision is: 1/41 or nearly 2.44%.

The minimum the company must charge for fire insurance and still maintain a positive expected value is calculated as:

The average cost to build a home in the subdivision * the chance of a wildfire destroying all the homes in the subdivision = 92,297 * 2.44% = $2,252.

So, the answer is $2,252.