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In Exercises 9鈥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.

惭肠顿辞苍补濒诲鈥檚

Burger King

奥别苍诲测鈥檚

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 惭肠顿辞苍补濒诲鈥檚 or an order that is accurate. Are the events of selecting an order from 惭肠顿辞苍补濒诲鈥檚 and selecting an accurate order disjoint events?

Short Answer

Expert verified

The probability of getting an order from 惭肠顿辞苍补濒诲鈥檚 or an accurate order is equal to 0.9123.

No, these two events are not disjoint.

Step by step solution

01

Given information

The given data depicts the number of food orders from four different outlets under two categories, accurate order and inaccurate order, in a tabulated form.

02

Addition rule of probability

For two events, A and B, the probability is that either event A, B or both occur. It has the following expression:

PAorB=PA+PB-PAandB

03

Disjoint events

Two events are said to be disjoint if theyboth cannot occur together.

That is,

PAandB=0

04

Calculation

The following table shows all the subtotals and the grand total:

惭肠顿辞苍补濒诲鈥檚

Burger King

奥别苍诲测鈥檚

Taco Bell

Totals

Order Accurate

329

264

249

145

987

Order Not Accurate

33

54

31

13

131

Totals

362

318

280

158

1118

Let E be the event of getting a food order from 惭肠顿辞苍补濒诲鈥檚.

Let F be the event of getting an accurate food order.

The total number of food orders is equal to 1,118.

The number of food orders from 惭肠顿辞苍补濒诲鈥檚 is calculated as shown below:

329+33=362

The number of accurate food orders is calculated as shown below:

329+264+249+145=987

The number of accurate food orders from 惭肠顿辞苍补濒诲鈥檚 is 329.

So, the required probabilities are obtained as shown below:

PE=3621118

PF=9871118

PEandF=3291118

Now, the probability (E or F) is as follows:

PEorF=PE+PF-PEandF=3621118+9871118-3291118=10201118=0.9123

Therefore, the probability of getting a food order from 惭肠顿辞苍补濒诲鈥檚 or getting an accurate food order is equal to0.912.

05

Identifying the disjoint property

Since the event of getting a food order from 惭肠顿辞苍补濒诲鈥檚 can occur simultaneously with the event of getting an accurate order, the given two events are not disjoint.

Mathematically,

PEandF=32911180

Thus, the events are not disjoint.

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