Sure, let's solve this step by step.
First, we need to calculate the total number of large orders. According to the table:
- Large Hot Dogs = 3
- Large Hamburgers = 18
- Large Sandwiches = 6
Adding these together gives us the total number of large orders:
[tex]\[
3 + 18 + 6 = 27
\][/tex]
Next, we calculate the total number of all orders. We'll sum up both the standard and large orders:
- Standard Hot Dogs = 9
- Standard Hamburgers = 45
- Standard Sandwiches = 19
- Large Hot Dogs = 3
- Large Hamburgers = 18
- Large Sandwiches = 6
Adding all these together:
[tex]\[
9 + 45 + 19 + 3 + 18 + 6 = 100
\][/tex]
Now, to find the probability that a randomly chosen order will be large, we use the formula:
[tex]\[
P (\text{Large}) = \frac{\text{Total Large Orders}}{\text{Total Orders}} = \frac{27}{100}
\][/tex]
Hence, the values we have are:
[tex]\[
P (\text{Large}) = \frac{27}{100}
\][/tex]
So, the detailed, step-by-step solution to find the probability that a chosen order will be large is:
[tex]\[
P (\text{Large}) = \frac{27}{100} = 0.27
\][/tex]
