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8.1-8.2 Quiz

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• 1. Winter Storm

The table shows the probabilities of a winter storm in New York for several months. Complete the table. Then describe the likelihood of each event in words.

• Worked-Out Solution

Remember that a probability is measured from 0 (impossible) to 1 (certain). Each of the probabilities in the table are less than 50%. So, each event is more unlikely than it is likely.

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```           _    _     _____    __   __    _  __
___   | || | ||  |__  //   \ \\/ //  | |/ //
/   || | || | ||    / //     \ ` //   | ' //
| [] || | \\_/ ||   / //__     | ||    | . \\
\__ ||  \____//   /_____||    |_||    |_|\_\\
-|_||   `---`    `-----`     `-`'    `-` --`
`-`
```
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• 2. Snowfall in Billings

Describe the likelihood that at least 1 inch of snow will accumulate in Billings.

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

```
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• 3. Snowfall in Helena

Describe the likelihood that at least 1 inch of snow will accumulate in Helena.

• Worked-Out Solution

The map indicates that the probability that at least 1 inch of snow will accumulate in Helena is about 80%. So, this event is likely.

Helena is the capital of Montana.

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

```
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• 4. Snowfall in Sidney

Describe the likelihood that at least 1 inch of snow will accumulate in Sidney.

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

```
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• 5. Snowfall in Opheim

Describe the likelihood that at least 1 inch of snow will accumulate in Opheim.

• Worked-Out Solution

The map indicates that the probability that at least 1 inch of snow will accumulate in Opheim is only about 1%. So, this event is nearly impossible.

Opheim is a small town near the Canadian border in Montana. Its population is about 100 people. Although it is cold in the winter, it is also dry. That is the reason the probability of snow is so low.

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```  ____       ___               _    _     _  _
|  _ \\    / _ \\      ___   | || | ||  | \| ||
| |_| ||  | / \ ||    /   || | || | ||  |  ' ||
| .  //   | \_/ ||   | [] || | \\_/ ||  | .  ||
|_|\_\\    \___//     \__ ||  \____//   |_|\_||
`-` --`    `---`       -|_||   `---`    `-` -`
`-`
```
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• 6. Counting the Number of Possibilities

Consider a computer that randomly selects a 4-digit number. Each digit can be any number from 0 through 9. How many possible numbers are there?

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```__    __     ___                 ___      ______
\ \\ / //   / _ \\    ____      / _ \\   /_   _//
\ \/ //   / //\ \\  |    \\   / //\ \\    | ||
\  //   |  ___  || | [] ||  |  ___  ||  _| ||
\//    |_||  |_|| |  __//  |_||  |_|| /__//
`     `-`   `-`  |_|`-`   `-`   `-`  `--`
`-`
```
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• 7. Finding a Theoretical Probability

Consider a computer that randomly selects a 4-digit number. Each digit can be any number from 0 through 9. Find the probability that the number is greater than or equal to 3000.

• Worked-Out Solution

There are 10,000 possible 4-digit numbers. They range from 0000 to 9999.

Of these, 7000 numbers are greater than or equal to 3000. These numbers range from 3000 to 9999.

So, the probability that the number is greater than or equal to 3000 is

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``` _    _     ______              _____    _    _
| |  | ||  /_   _//   ____     |  ___|| | \  / ||
| |/\| ||   -| ||-   |    \\   | ||__   |  \/  ||
|  /\  ||   _| ||_   | [] ||   | ||__   | .  . ||
|_// \_||  /_____//  |  __//   |_____|| |_|\/|_||
`-`   `-`  `-----`   |_|`-`    `-----`  `-`  `-`
`-`
```
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• 8. Finding a Theoretical Probability

Consider a computer that randomly selects a 4-digit number. Each digit can be any number from 0 through 9. Find the probability that the number is divisible by 1000.

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``` _    _      ___      ______     ___     _    _
| |  | ||   / _ \\   /_   _//   / _ \\  | |  | ||
| |/\| ||  / //\ \\    | ||    / //\ \\ | |/\| ||
|  /\  || |  ___  ||  _| ||   |  ___  |||  /\  ||
|_// \_|| |_||  |_|| /__//    |_||  |_|||_// \_||
`-`   `-` `-`   `-`  `--`     `-`   `-` `-`   `-`

```
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