To correct the clerk's error and organize the sample space for the clothing store's shirts based on color and sleeve styles, we can create a table that systematically lists all combinations of sleeve styles (long, short, no) and colors (pink, teal, red).
First, let's define the variables:
- Sleeve Types: Long (L), Short (S), No Sleeve (N)
- Colors: Pink (P), Teal (T), Red (R)
Now, we can construct a complete sample space by identifying all combinations of the colors and sleeve styles.
Here’s how the complete sample space looks:
| Sleeve Style | Color | |--------------|---------| | Long | Pink | (L,P) | | Long | Teal | (L,T) | | Long | Red | (L,R) | | Short | Pink | (S,P) | | Short | Teal | (S,T) | | Short | Red | (S,R) | | No Sleeve | Pink | (N,P) | | No Sleeve | Teal | (N,T) | | No Sleeve | Red | (N,R) |
Thus, the complete sample space includes the following combinations:
- (Long, Pink)
- (Long, Teal)
- (Long, Red)
- (Short, Pink)
- (Short, Teal)
- (Short, Red)
- (No Sleeve, Pink)
- (No Sleeve, Teal)
- (No Sleeve, Red)
Error Analysis:
The clerk's error was that they only listed combinations involving long and short sleeves but ignored the "no sleeve" style entirely, which led to an incomplete representation of the sample space. Therefore, the correct sample space should include all three sleeve types with all three colors.