To solve the problem of finding the probability that a randomly chosen customer's order will be Large, we follow these steps:
1. Identify the number of each type of order:
- Standard Hot Dog = 9
- Standard Hamburger = 45
- Standard Sandwich = 19
- Large Hot Dog = 3
- Large Hamburger = 18
- Large Sandwich = 6
2. Calculate the total number of Large orders:
- Large orders are given by:
[tex]\[
\text{Large Hot Dog} + \text{Large Hamburger} + \text{Large Sandwich} = 3 + 18 + 6 = 27
\][/tex]
Thus, the total number of Large orders is 27.
3. Calculate the total number of all orders:
- The total number of orders is the sum of all Standard and Large orders:
[tex]\[
\text{Standard Hot Dog} + \text{Standard Hamburger} + \text{Standard Sandwich} + \text{Large Hot Dog} + \text{Large Hamburger} + \text{Large Sandwich}
\][/tex]
- Plugging in the numbers:
[tex]\[
9 + 45 + 19 + 3 + 18 + 6 = 100
\][/tex]
Thus, the total number of orders is 100.
4. Calculate the probability of a Large order:
- The probability that a randomly chosen order is Large is given by the ratio of the total number of Large orders to the total number of orders:
[tex]\[
P(\text{Large}) = \frac{\text{Total Large orders}}{\text{Total orders}} = \frac{27}{100}
\][/tex]
Therefore, the probability [tex]\( P(\text{Large}) \)[/tex] that a randomly chosen customer's order will be Large is:
[tex]\[
P(\text{Large}) = 0.27
\][/tex]
So, the probability is [tex]\(\boxed{0.27}\)[/tex].
