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Given the table below:

[tex]\[
\begin{tabular}{|c|c|c|c|}
\hline
& Hot Dog & Hamburger & Sandwich \\
\hline
Standard & 9 & 45 & 19 \\
\hline
Large & 3 & 18 & 6 \\
\hline
\end{tabular}
\][/tex]

What is the probability that a randomly chosen customer ordered a Large item?

[tex]\[
P (\text{Large}) = \frac{\text{Total Large orders}}{\text{Total orders}} = \frac{[?]}{\square}
\][/tex]



Answer :

GinnyAnswer
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]

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