### 8.2 Estimating Likelihood

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• 23. Comparing Probabilities

You randomly choose a card from a standard deck of playing cards. Find the theoretical probability of choosing a card of each suit.

• Worked-Out Solution

There are 52 cards in the deck and 13 of each suit. So, the probability of drawing any particular suit is

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

```
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• 24. Comparing Probabilities

You have a standard deck of cards. The bar graph shows the results of randomly choosing 1 card, recording its suit, and placing it back in the deck for 50 trials. Find the experimental probability of choosing a card of each suit.

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

```
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• 25. Comparing Probabilities

Compare the probabilities found in Exercises 23 and 24.

• Worked-Out Solution

The theoretical and experimental probabilities for drawing each suit are as follows.

Anyone who has played cards recognizes that a theoretical probability is the result you expect over hundreds or even thousands of card hands. For a small number of hands (like 50), the results can vary. This is the whole point of card games, isn't it? You are hoping that you will have good "luck" and that your "experimental probability" will be better than the average.

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

```
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• 26. Addition Rule

The probability that one of two events occurs is

You randomly choose a card from a standard deck of cards. Find the probability of choosing a heart or a 6.

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```  _____      ___               __   __  __    __
/ ____||   / _ \\    ____     \ \\/ // \ \\ / //
/ //---`'  / //\ \\  |    \\    \ ` //   \ \/ //
\ \\___   |  ___  || | [] ||     | ||     \  //
\_____|| |_||  |_|| |  __//     |_||      \//
`----`  `-`   `-`  |_|`-`      `-`'       `
`-`
```
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• 27. Addition Rule

The probability that one of two events occurs is

You randomly choose a card from a standard deck of cards. Find the probability that the card is black or a 2.

• Worked-Out Solution

Here are the individual probabilities.

So the probability of drawing a black card or a 2 is about

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

```
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• 28. Addition Rule

The probability that one of two events occurs is

You randomly choose a card from a standard deck of cards. Find the probability of choosing a face card or a diamond.

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