Question

In Exercises 9–20, use the data in the following table, which lists drive-thru order accuracy at popular fast food chains (data from a QSR Drive-Thru Study). Assume that orders are randomly selected from those included in the table.

	McDonald’s	Burger King	Wendy’s	Taco Bell
Order Accurate	329	264	249	145
OrderNotAccurate	33	54	31	13

Fast Food Drive-Thru Accuracy If one order is selected, find the probability of getting an order from Burger King or Taco Bell or an order that is accurate.

Short answer

The probability of getting an order from Burger King or Taco Bell or an accurate order is equal to 0.943.

Step-by-step solution

Given information

The number of food orders at drive-thru centres of four fast-food chains are provided.

Some orders are accurate, while others are inaccurate.

Addition rule of probability

For three events, A, B, and C, to occur individually or simultaneously, the following probability is calculated:

$P\left(A\text{or}B\text{or}C\right)=P\left(A\right)+P\left(B\right)+P\left(C\right)-P\left(A\text{and}B\right)-P\left(A\text{and}C\right)-P\left(B\text{and}C\right)$

Calculation

The subtotals for each chain are tabulated below:

	McDonald’s	Burger King	Wendy’s	Taco Bell	Totals
Order Accurate	329	264	249	145	987
Order Not Accurate	33	54	31	13	131
Totals	362	318	280	158	Grand Total=1118

The total number of food orders is equal to 1118.

Let E be the event of selecting a food order from Burger King.

Let F be the event of selecting a food order from Taco Bell.

Let G be the event of selecting an accurate food order.

The number of food orders from Burger King is equal to 318.

The probability of selecting a food order from Burger King,

$P\left(E\right)=\frac{318}{1118}$

The number of food orders from Taco Bell is equals 158.

The probability of selecting a food order from Taco Bell,

.$P\left(F\right)=\frac{158}{1118}$

The number of accurate food orders is equal to 987.

The probability of selecting an accurate food order,

$P\left(G\right)=\frac{987}{1118}$

The number of orders from Burger King and Taco Bell is equal to 0. Thus,

.$P\left(E\text{and}F\right)=\frac{0}{1118}$

The number of accurate orders from Burger King is equal to 264. Thus,

$P\left(E\text{and}G\right)=\frac{264}{1118}$

The number of accurate orders from Taco Bell is equal to 145. Thus,

$P\left(F\text{and}G\right)=\frac{145}{1118}$

.

The probability of getting an order from Burger King or Taco Bell or an accurate order is calculated as follows:

$$\begin{gathered} P\left(E\text{or}F\text{or}G\right)=P\left(E\right)+P\left(F\right)+P\left(G\right)-P\left(E\text{and}F\right)-P\left(E\text{and}G\right)-P\left(F\text{and}G\right) \\ =\frac{318}{1118}+\frac{158}{1118}+\frac{987}{1118}-\frac{0}{1118}-\frac{264}{1118}-\frac{145}{1118} \\ =\frac{1054}{1118} \\ =0.9428 \end{gathered}$$

Therefore, the probability ofgetting an order from Burger King or Taco Bell or an accurate orderis equal to0.943.