Chapter 8 Review Exercises

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• 7. Platonic Solids

There are five Platonic solids: tetrahedron, cube, octahedron, dodecahedron, and icosahedron.

Why do these solids make natural shapes for dice?

• Worked-Out Solution

Each of the Platonic solids is a natural shape for dice because, for each solid, the probability of landing on any one of the faces is the same.

For instance, with a tetrahedron, each of the four faces has a one-fourth chance of landing down.

With a cube, each of the six faces has a one-sixth chance of landing down (or landing up).

In 1984, the author of this textbook patented a type of dice using dodecahedrons. The twelve faces have countable, recessed "dots" numbering one to six. Each total from one to six appears on precisely two opposite faces.

To view the patent and a sketch of the dice, go to http://math.andyou.com/pdf/patent.pdf

If you would like a pair of these dice, you can write to Jackie at feedback@AndYou.com. She will send you a pair free, while the supply lasts.

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

```
• 8. Platonic Solids

There are five Platonic solids: tetrahedron, cube, octahedron, dodecahedron and icosahedron.

Which shape is the best for dice? Why? Which is the worst? Why?

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```  ______    ______   __   _     _____    _    _
/_____//  /_   _// | || | ||  |  ___|| | || | ||
`____ `    -| ||-  | '--' ||  | ||__   | || | ||
/___//     _| ||_  | .--. ||  | ||__   | \\_/ ||
`__ `     /_____// |_|| |_||  |_____||  \____//
/_//      `-----`  `-`  `-`   `-----`    `---`
`-`
```
• 9. Platonic Solids

There are five Platonic solids: tetrahedron, cube, octahedron, dodecahedron, and icosahedron.

A die has the shape of an icosahedron, with consecutively numbered sides starting at 1. What is the probability of rolling a number that is greater than 5?

• Worked-Out Solution

An icosahedron die has 20 sides, numbered

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20.

When such a die is rolled, the probability of rolling a number greater than 5 is

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``` __   __    ______   _____     __   __    ______
\ \\/ //  /_   _// |  __ \\   \ \\/ //  /_____//
\   //    -| ||-  | |  \ ||   \ ` //   `____ `
/ . \\    _| ||_  | |__/ ||    | ||    /___//
/_//\_\\  /_____// |_____//     |_||    `__ `
`-`  --`  `-----`   -----`      `-`'    /_//
`-`
```
• 10. Platonic Solids

There are only five Platonic solids. What is the definition of a Platonic solid?

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

```
• 11. Finding an Experimental Probability

The tables show the results of a survey that asked adults whether they own an MP3 player.

Find the probability that an adult in each age group owns an MP3 player. Then describe the likelihood.

• Worked-Out Solution

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```  _____     _____               _____      _____
/ ____||  |  ___||   ____     |  ___||   / ___//
/ //---`'  | ||__    |    \\   | ||__     \___ \\
\ \\___    | ||__    | [] ||   | ||__     /    //
\_____||  |_____||  |  __//   |_____||  /____//
`----`   `-----`   |_|`-`    `-----`  `-----`
`-`
```
• 12. Finding an Experimental Probability

The tables show the results of a survey that asked adults whether they own an MP3 player.

Find the probability that an adult in each geographic location owns an MP3 player. Then describe the likelihood.

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```  ____      ______    ____     __   __   _    _