4. Simulations
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The sample space of an experiment is the set of all possible outcomes.
Example Table:
| Nickels | Dimes | Quarters |
|---|---|---|
| 10 | 0 | 0 |
| 8 | 1 | 0 |
| 6 | 2 | 0 |
| 4 | 3 | 0 |
| 2 | 4 | 0 |
| 0 | 5 | 0 |
| 5 | 0 | 1 |
| 0 | 0 | 2 |
| 1 | 2 | 1 |
| 3 | 1 | 1 |
We are given an experiment and want to represent the sample space by making a table. First, let's consider the situation from the exercise.
|
Dana received $25 for her birthday and spent $24.50 on a DVD. |
| Coin | Number of Cents |
|---|---|
| Nickel | 5 |
| Dime | 10 |
| Quarter | 25 |
Now, let's focus on finding the sample space. The sample space of an experiment is the set of all possible outcomes. To make the table, we will list the types of coins in the top row, and each row will represent a combination of coins that add up to $0.50.
| Nickels | Dimes | Quarters |
|---|---|---|
| 10 | 0 | 0 |
| 8 | 1 | 0 |
| 6 | 2 | 0 |
| 4 | 3 | 0 |
| 2 | 4 | 0 |
| 0 | 5 | 0 |
| 5 | 0 | 1 |
| 0 | 0 | 2 |
| 1 | 2 | 1 |
| 3 | 1 | 1 |
Keep in mind that there are several ways to make a table. The part that matters most is that the sample space ends up with all of the possible combinations.