### 8.2 Estimating Likelihood

<
>
• 17. Football

The graph shows the positions of the most valuable players (MVPs) for the first 45 Super Bowls. (Note: There are 46 players in the graph because there were co-MVPs in Super Bowl XII.)

Find the probability that a quarterback is a Super Bowl MVP. (See Example 5 and Example 6.)

• Worked-Out Solution

The total number of MVPs in Super Bowl history is

Of these, 24 have been quarterbacks. Based on this data, the probability that the most valuable player in a Super Bowl will be a quarterback is

These comments are not screened before publication. Constructive debate about the information on this page is welcome, but personal attacks are not. Please do not post comments that are commercial in nature or that violate copyright. Comments that we regard as obscene, defamatory, or intended to incite violence will be removed. If you find a comment offensive, you may flag it.

```           __   __   _    _    _    _     _  _
___    \ \\/ // | \  / || | || | ||  | \| ||
/   ||   \ ` //  |  \/  || | || | ||  |  ' ||
| [] ||    | ||   | .  . || | \\_/ ||  | .  ||
\__ ||    |_||   |_|\/|_||  \____//   |_|\_||
-|_||    `-`'   `-`  `-`    `---`    `-` -`
`-`
```
• 18. Football

The graph shows the positions of the most valuable players (MVPs) for the first 45 Super Bowls. (Note: There are 46 players in the graph because there were co-MVPs in Super Bowl XII.)

Find the probability that an offensive player (quarterback, running back, or wide receiver) is a Super Bowl MVP. (See Example 5 and Example 6.)

These comments are not screened before publication. Constructive debate about the information on this page is welcome, but personal attacks are not. Please do not post comments that are commercial in nature or that violate copyright. Comments that we regard as obscene, defamatory, or intended to incite violence will be removed. If you find a comment offensive, you may flag it.

```  _____     _____     ______   __   __
/  ___||  |  ___||  /_   _//  \ \\/ //   ____
| // __    | ||__      | ||     \ ` //   |    \\
| \\_\ ||  | ||__     _| ||      | ||    | [] ||
\____//   |_____||  /__//       |_||    |  __//
`---`    `-----`   `--`        `-`'    |_|`-`
`-`
```
• 19. Football

The graph shows the positions of the most valuable players (MVPs) for the first 45 Super Bowls. (Note: There are 46 players in the graph because there were co-MVPs in Super Bowl XII.)

Find the probability that a defensive or special teams player (defensive lineman, linebacker, safety, cornerback, or kick returner) is a Super Bowl MVP. (See Example 5 and Example 6.)

• Worked-Out Solution

The total number of MVPs in Super Bowl history is

The number of defensive or special teams players is

Based on this data, the probability that the most valuable player in a Super Bowl will be a defensive or special teams player is

These comments are not screened before publication. Constructive debate about the information on this page is welcome, but personal attacks are not. Please do not post comments that are commercial in nature or that violate copyright. Comments that we regard as obscene, defamatory, or intended to incite violence will be removed. If you find a comment offensive, you may flag it.

``` __   _      ___               __   __   _____
| || | ||   / _ \\      ___    \ \\/ // |  __ \\
| '--' ||  | / \ ||    /   ||   \ ` //  | |  \ ||
| .--. ||  | \_/ ||   | [] ||    | ||   | |__/ ||
|_|| |_||   \___//     \__ ||    |_||   |_____//
`-`  `-`    `---`       -|_||    `-`'    -----`
`-`
```
• 20. Football

The graph shows the positions of the most valuable players (MVPs) for the first 45 Super Bowls. (Note: There are 46 players in the graph because there were co-MVPs in Super Bowl XII.)

How many times more likely is it for a Super Bowl MVP to be a quarterback than a wide receiver? (See Example 5 and Example 6.)

These comments are not screened before publication. Constructive debate about the information on this page is welcome, but personal attacks are not. Please do not post comments that are commercial in nature or that violate copyright. Comments that we regard as obscene, defamatory, or intended to incite violence will be removed. If you find a comment offensive, you may flag it.

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

```
• 21. Football

The graph shows the positions of the most valuable players (MVPs) for the first 45 Super Bowls. (Note: There are 46 players in the graph because there were co-MVPs in Super Bowl XII.)

How many times more likely is it for a Super Bowl MVP to be a running back than a linebacker? (See Example 5 and Example 6.)

• Worked-Out Solution

The total number of MVPs in Super Bowl history is

Based on this data, find the probabilities that the most valuable player in a Super Bowl will be a running back or a linebacker.

So, it is about 3.5 times more likely that a Super Bowl MVP will be a running back than a linebacker.

These comments are not screened before publication. Constructive debate about the information on this page is welcome, but personal attacks are not. Please do not post comments that are commercial in nature or that violate copyright. Comments that we regard as obscene, defamatory, or intended to incite violence will be removed. If you find a comment offensive, you may flag it.

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

```
• 22. Football

The graph shows the positions of the most valuable players (MVPs) for the first 45 Super Bowls. (Note: There are 46 players in the graph because there were co-MVPs in Super Bowl XII.)

How many times more likely is it for a Super Bowl MVP to be a quarterback than a defensive or special teams player? (See Example 5 and Example 6.)

These comments are not screened before publication. Constructive debate about the information on this page is welcome, but personal attacks are not. Please do not post comments that are commercial in nature or that violate copyright. Comments that we regard as obscene, defamatory, or intended to incite violence will be removed. If you find a comment offensive, you may flag it.
```             ___      _____      ___