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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 Burger King or Taco Bell or an order that is accurate.

Short Answer

Expert verified

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

01

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.

02

Addition rule of probability

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

PAorBorC=PA+PB+PC-PAandB-PAandC-PBandC

03

Calculation

The subtotals for each chain are tabulated below:

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.

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,

PE=3181118

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

The probability of selecting a food order from Taco Bell,

.PF=1581118

The number of accurate food orders is equal to 987.

The probability of selecting an accurate food order,

PG=9871118

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

.PEandF=01118

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

PEandG=2641118

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

PFandG=1451118

.

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

PEorForG=PE+PF+PG-PEandF-PEandG-PFandG=3181118+1581118+9871118-01118-2641118-1451118=10541118=0.9428

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

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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?

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