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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 three different orders are selected, find the probability that they are all from 奥别苍诲测鈥檚

Short Answer

Expert verified

The probability that all three orders are from 奥别苍诲测鈥檚 is equal to 0.0156.

Step by step solution

01

Given information

The given data shows the number of food orders at drive-thru centers of four fastfood chains.

02

Multiplication rule of probability

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

PAandBandC=PAPBPC

03

Calculation

The table below shows the subtotals for each category:

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

Grand

Total=1118

The total number of food orders is equal to 1118.

Define the events.

Let E be the event of selecting a food order from 奥别苍诲测鈥檚 on the first selection.

Let Fbe the event of selecting a food order from 奥别苍诲测鈥檚 on the second selection.

Let G be the event of selecting a food order from 奥别苍诲测鈥檚 on the third selection.

The number of food orders from 奥别苍诲测鈥檚 is equal to 318.

The probability of selecting a food order from 奥别苍诲测鈥檚 on the first selection is equal to:

PE=2801118

As the remaining total number of orders and the remaining number of orders from 奥别苍诲测鈥檚 will be decreased by 1, the probability of selecting a food order from 奥别苍诲测鈥檚 on the second selection is equal to:

PF=2791117

Further, the remaining total number of orders and the remaining number of orders from 奥别苍诲测鈥檚 will again decrease by 1. Thus, the probability of selecting a food order from 奥别苍诲测鈥檚 on the third selection is equal to:

PG=2781116

The probability of selecting three orders from 奥别苍诲测鈥檚 is given by:

PEandFandG=PEPFPG=280111827911172761116=0.0156

Therefore, the probability of selecting three orders from 奥别苍诲测鈥檚 is equal to 0.0156.

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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 two orders are selected, find the probability that they are both from Taco Bell.

a. Assume that the selections are made with replacement. Are the events independent?

b. Assume that the selections are made without replacement. Are the events independent?

In Exercises 17鈥20, refer to the accompanying table showing results from a Chembio test for hepatitis C among HIV-infected patients (based on data from a variety of sources).

Positive Test Result

Negative Test Result

Hepatitis C

335

10

No Hepatitis C

2

1153

Negative Predictive Value Find the negative predictive value for the test. That is, find the probability that a subject does not have hepatitis C, given that the test yields a negative result. Does the result make the test appear to be effective?

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