Let's break down the problem step by step to find the probability that a randomly chosen customer's order will be both Standard and a Hamburger:
1. Understand the given data:
- The survey details the number of orders for various categories.
- We have categories: Hot Dog, Hamburger, and Sandwich.
- Each category is further divided into Standard and Large sizes.
2. Extract the specific numbers from the table:
- For Standard Hot Dog, there are 9 orders.
- For Standard Hamburger, there are 45 orders.
- For Standard Sandwich, there are 19 orders.
- For Large Hot Dog, there are 3 orders.
- For Large Hamburger, there are 18 orders.
- For Large Sandwich, there are 6 orders.
3. Calculate the total number of orders:
- Sum up all orders: [tex]\(9 + 45 + 19 + 3 + 18 + 6 = 100\)[/tex].
- This gives us the total number of orders as [tex]\(100\)[/tex].
4. Find the specific number of Standard Hamburger orders:
- From the given data, there are [tex]\(45\)[/tex] orders for Standard Hamburger.
5. Calculate the probability:
- The probability [tex]\(P(\text{Standard} \cap \text{Hamburger})\)[/tex] is the ratio of the number of Standard Hamburger orders to the total number of orders.
- Therefore, the probability is:
[tex]\[
P(\text{Standard} \cap \text{Hamburger}) = \frac{\text{Standard Hamburger Orders}}{\text{Total Orders}} = \frac{45}{100} = 0.45
\][/tex]
Conclusion:
The probability that a customer chosen at random ordered a Standard Hamburger is [tex]\(0.45\)[/tex].
