Let's analyze the given table to understand what the 0.1 in the highlighted cell represents.
The table displays the relationship between customers ordering desserts and appetizers. The cells in the table contain proportions of customers. We can see the following:
1. The total proportion of customers is 1.0.
2. The proportion of customers who ordered both dessert and appetizer is 0.1.
3. The proportion of customers who ordered dessert but not appetizer is 0.3.
4. The proportion of customers who did not order dessert but ordered appetizer is 0.2.
5. The proportion of customers who neither ordered dessert nor appetizer is 0.4.
### Understanding the Options:
Option A: [tex]$10 \%$[/tex] of her customers ordered dessert.
- The total proportion of customers who ordered dessert (sum of proportions in the dessert row) is 0.4 (0.1 who ordered appetizer and dessert, and 0.3 who did not order appetizer but ordered dessert).
- Therefore, 0.1 cannot represent the proportion of customers who ordered dessert, since that's 0.4 or 40%.
Option B: [tex]$10 \%$[/tex] of her customers ordered an appetizer and dessert.
- The cell in question (0.1) represents customers who ordered both appetizer and dessert.
- Since this cell is 0.1, it means 10% of the customers ordered both appetizer and dessert.
- This interpretation fits exactly, making B a potential correct answer.
Option C: [tex]$10 \%$[/tex] of the customers who ordered an appetizer ordered dessert.
- To verify this, we look at the total proportion of customers who ordered appetizers, which is 0.3 (sum of proportions in the appetizer column).
- Now we need the proportion of customers who ordered both appetizer and dessert, which is 0.1.
- So, the proportion of those who ordered an appetizer and then dessert = [tex]\( \frac{0.1}{0.3} = \frac{1}{3} \approx 33.3\% \)[/tex].
- This shows that 33.3% of the customers who ordered an appetizer also ordered dessert, not 10%.
Option D: [tex]$10 \%$[/tex] of her customers ordered an appetizer.
- The total proportion of customers who ordered any kind of appetizer (sum of appetizer column) is 0.3 or 30%.
- This does not align with 0.1 representing the percentage of customers who ordered an appetizer.
### Conclusion:
Option B is the correct interpretation of the 0.1 in the highlighted cell.
So, the answer is:
B. [tex]$10 \%$[/tex] of her customers ordered an appetizer and dessert.
