Problem

Use the data in the following table, which lists drive-thru order accuracy at popular fast food chains. Assume that orders are randomly selected from those included in the table Drive-thru Restaurant $\mathrm{o}$ \begin{tabular}{|l|c|c|c|c|} \hline & A & B & C & D \\ \hline Order Accurate & 324 & 266 & 236 & 122 \\ \hline Order Not Accurate & 34 & 59 & 35 & 20 \\ \hline \end{tabular} If three different orders are selected, find the probability that they are all from Restaurant A.

Solution

Step 1 :First, we need to find the total number of orders from all restaurants. This is done by adding the number of orders from each restaurant. In this case, we have \(324 + 34\) orders from Restaurant A, \(266 + 59\) orders from Restaurant B, \(236 + 35\) orders from Restaurant C, and \(122 + 20\) orders from Restaurant D. This gives us a total of \(1096\) orders.

Step 2 :Next, we need to find the number of ways to select three orders from Restaurant A. This is given as \(45498936\).

Step 3 :Finally, we can find the probability by dividing the number of ways to select three orders from Restaurant A by the total number of orders. This gives us a probability of approximately \(0.0346544687395977\).

Step 4 :\(\boxed{0.0347}\) is the final answer, which represents the probability that all three orders are from Restaurant A.

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Source: https://solvelyapp.com/problems/28801/

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