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 \begin{tabular}{|l|c|c|c|c|} \hline & A & B & C & D \\ \hline Order Accurate & 330 & 270 & 233 & 132 \\ \hline Order Not Accurate & 33 & 50 & 38 & 14 \\ \hline \end{tabular} If one order is selected, find the probability of getting an order from Restaurant A or an order that is accurate. Are the events of selecting an order from Restaurant A and selecting an accurate order disjoint events? The probability of getting an order from kestaurant A or an order that is accurate is (Round to three decimal places as needed.) Are the events of selecting an order from Restaurant A and selecting an accurate order disjoint events? The events are not disjoint because it is possible to receive an accurate order from Restaurant A.

Solution

Step 1 :First, calculate the total number of orders from all restaurants. This is done by adding the number of accurate and not accurate orders from each restaurant. The total number of orders is \(363 + 320 + 271 + 146 = 1100\).

Step 2 :Next, calculate the total number of accurate orders from all restaurants. This is done by adding the number of accurate orders from each restaurant. The total number of accurate orders is \(330 + 270 + 233 + 132 = 965\).

Step 3 :Calculate the probability of getting an order from Restaurant A. This is done by dividing the total number of orders from Restaurant A by the total number of orders. The probability is \(\frac{363}{1100} = 0.33\).

Step 4 :Calculate the probability of getting an accurate order. This is done by dividing the total number of accurate orders by the total number of orders. The probability is \(\frac{965}{1100} = 0.877\).

Step 5 :Calculate the probability of getting an accurate order from Restaurant A. This is done by dividing the number of accurate orders from Restaurant A by the total number of orders. The probability is \(\frac{330}{1100} = 0.3\).

Step 6 :Finally, calculate the probability of getting an order from Restaurant A or an accurate order. This is done by adding the probability of getting an order from Restaurant A and the probability of getting an accurate order, then subtracting the probability of getting an accurate order from Restaurant A (since these orders are counted twice). The probability is \(0.33 + 0.877 - 0.3 = 0.907\).

Step 7 :Final Answer: The probability of getting an order from Restaurant A or an order that is accurate is approximately \(\boxed{0.907}\). The events of selecting an order from Restaurant A and selecting an accurate order are not disjoint events because it is possible to receive an accurate order from Restaurant A.

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