To find the probability that a randomly chosen customer's order will be both a Standard size and include a Hamburger, let's follow these steps:
1. Identify the total number of Standard Hamburgers:
From the given table, we see that there are 45 Standard Hamburgers.
2. Calculate the total number of orders:
Add up all the orders from the table:
- Standard Hot Dog: 9
- Standard Hamburger: 45
- Standard Sandwich: 19
- Large Hot Dog: 3
- Large Hamburger: 18
- Large Sandwich: 6
Total number of orders [tex]\( = 9 + 45 + 19 + 3 + 18 + 6 = 100 \)[/tex].
3. Determine the probability:
The probability of choosing a customer who ordered a Standard Hamburger is given by the ratio of the number of Standard Hamburger orders to the total number of orders.
[tex]\[
P (\text{Standard} \cap \text{Hamburger}) = \frac{\text{Number of Standard Hamburger orders}}{\text{Total number of orders}} = \frac{45}{100}
\][/tex]
4. Simplify the fraction if necessary:
The fraction [tex]\(\frac{45}{100}\)[/tex] can be simplified if required:
- The greatest common divisor (GCD) of 45 and 100 is 5.
- Thus, [tex]\( \frac{45 \div 5}{100 \div 5} = \frac{9}{20} \)[/tex].
So, the simplified probability can also be expressed as [tex]\(\frac{9}{20}\)[/tex], but since we are asked for the decimal form:
[tex]\[
\frac{45}{100} = 0.45
\][/tex]
Thus, the probability that a randomly chosen customer's order will be Standard and a Hamburger is [tex]\(0.45\)[/tex] or [tex]\(45\%\)[/tex].
