### Chapter 8 Review Exercises

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• 13. Fire Insurance

Assume that you are the owner of a home appliance company. You take out a \$500,000 fire insurance policy on your factory. The annual premium is \$2750. The probability of a fire is 0.005. What is the expected value?

• Worked-Out Solution

Notice that this is from the point of view of the policy holder.

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``` ______      ___     __   __    ______     _____
|      \\   / _ \\   \ \\/ //  /_   _//   / ___//
|  --  //  / //\ \\   \   //    -| ||-    \___ \\
|  --  \\ |  ___  ||  / . \\    _| ||_    /    //
|______// |_||  |_|| /_//\_\\  /_____//  /____//
`------`  `-`   `-`  `-`  --`  `-----`  `-----`

```
• 14. Flood Insurance

Assume that you are the owner of a home appliance company. You take out a \$250,000 flood insurance policy on your factory. The annual premium is \$3770. The probability of a flood is 0.014. What is the expected value?

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``` _    _    _    _     _  __    ______   ______
| || | || | || | ||  | |/ //  /_   _// |      \\
| || | || | || | ||  | ' //    -| ||-  |  --  //
| \\_/ || | \\_/ ||  | . \\    _| ||_  |  --  \\
\____//   \____//   |_|\_\\  /_____// |______//
`---`     `---`    `-` --`  `-----`  `------`

```
• 15. Home Appliance Company

Your company is considering developing one of two toaster models. Use a decision tree to decide which model your company should develop.

• Worked-Out Solution

Based on this decision tree, your company has a better expected value by developing toaster A.

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```  _____    __   __    ____      ______   __   __
|__  //   \ \\/ //  |  _ \\   /_   _//  \ \\/ //
/ //     \ ` //   | |_| ||   -| ||-    \   //
/ //__     | ||    | .  //    _| ||_    / . \\
/_____||    |_||    |_|\_\\   /_____//  /_//\_\\
`-----`     `-`'    `-` --`   `-----`   `-`  --`

```
• 16. Home Appliance Company

Assume that you are the owner of a home appliance company. Your company is considering developing one of two microwave models. Use a decision tree to decide which model your company should develop.

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```  _____      ___     _    _      ___      ______
/  ___||   / _ \\  | || | ||   / _ \\   /_____//
| // __    / //\ \\ | || | ||  / //\ \\  `____ `
| \\_\ || |  ___  ||| \\_/ || |  ___  || /___//
\____//  |_||  |_|| \____//  |_||  |_|| `__ `
`---`   `-`   `-`   `---`   `-`   `-`  /_//
`-`
```
• 17. Option Comparison

Compare the two options.

• Worked-Out Solution

Based on this decision tree, option 2 has the greater expected value.

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``` _    _     ______    _  __     ___     _    _
| |  | ||  /_   _//  | |/ //   / _ \\  | || | ||
| |/\| ||   -| ||-   | ' //   | / \ || | || | ||
|  /\  ||   _| ||_   | . \\   | \_/ || | \\_/ ||
|_// \_||  /_____//  |_|\_\\   \___//   \____//
`-`   `-`  `-----`   `-` --`   `---`     `---`

```
• 18. Investment Comparison

You want to invest \$1000. Find the expected values for the two investments.

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```  ______   __   __   _    _    __   __   __   _
/_   _//  \ \\/ // | |  | ||  \ \\/ // | || | ||
`-| |,-    \ ` //  | |/\| ||   \ ` //  | '--' ||
| ||      | ||   |  /\  ||    | ||   | .--. ||
|_||      |_||   |_// \_||    |_||   |_|| |_||
`-`'      `-`'   `-`   `-`    `-`'   `-`  `-`

```