To determine the probability that a randomly chosen customer's order will be large, follow these steps:
1. Identify the total number of large orders.
- Number of large hot dogs ordered: 3
- Number of large hamburgers ordered: 18
- Number of large sandwiches ordered: 6
Therefore, the total number of large orders is:
[tex]\[
3 + 18 + 6 = 27
\][/tex]
2. Identify the overall total number of orders.
- Number of standard hot dogs ordered: 9
- Number of large hot dogs ordered: 3
- Number of standard hamburgers ordered: 45
- Number of large hamburgers ordered: 18
- Number of standard sandwiches ordered: 19
- Number of large sandwiches ordered: 6
Therefore, the total number of orders is:
[tex]\[
9 + 3 + 45 + 18 + 19 + 6 = 100
\][/tex]
3. Calculate the probability of choosing a large order.
[tex]\[
P(\text{Large}) = \frac{\text{Total Large orders}}{\text{Total orders}} = \frac{27}{100}
\][/tex]
Thus, the probability that a customer's order will be large, when chosen at random, is [tex]\( \boxed{0.27} \)[/tex].
