Question

Error Analysis A clothing store sells shirts with​ long, short, or no sleeves. Each style is available in teal​, gray​, or red. A clerk incorrectly states the sample space for the possible color and sleeve styles as left parenthesis teal comma long right parenthesis​, left parenthesis teal comma short right parenthesis​, left parenthesis teal comma no right parenthesis​, left parenthesis gray comma long right parenthesis​, left parenthesis gray comma short right parenthesis​, and left parenthesis gray comma no right parenthesis. Use a table to show the sample space. What error did the clerk​ make?
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Part 1
Complete the table that represents the sample space of color and sleeve styles combinations.
Sample Space
teal
gray
red
long
▼
gray
teal
red
​,
▼
no
long
short
▼
gray
teal
red
​,
▼
long
short
no
▼
red
gray
teal
​,
▼
short
no
long
short
▼
teal
red
gray
​,
▼
short
no
long
▼
red
gray
teal
​,
▼
long
short
no
▼
gray
teal
red
​,
▼
short
no
long
no
▼
gray
teal
red
​,
▼
no
short
long
▼
red
gray
teal
​,
▼
no
short
long
▼
red
teal
gray
​,
▼
long
short
no

Answer 1

To represent the sample space of the possible combinations of shirt styles (sleeves) and colors, we consider all the combinations based on the options given.

For this problem, we have:
- Sleeve styles: long, short, no
- Colors: teal, gray, red

### Sample Space Table

We can construct a table to display all the combinations:

| Sleeve Style | Color |
|--------------|--------|
| Long | Teal |
| Long | Gray |
| Long | Red |
| Short | Teal |
| Short | Gray |
| Short | Red |
| No | Teal |
| No | Gray |
| No | Red |

### Errors in Clerk's Statement

The clerk made an error by omitting combinations that involve the color red. The correct sample space should include combinations with the red color for each sleeve style. The clerk's stated sample space is missing:

- Long sleeves with red
- Short sleeves with red
- No sleeves with red

In total, there should be **9 combinations**, not **6** as reflected in the clerk's statement.