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In Exercises 5鈥36, express all probabilities as fractions.

Safety with Numbers The author owns a safe in which he stores all of his great ideas for the next edition of this book. The safe 鈥渃ombination鈥 consists of four numbers between 0 and 99, and the safe is designed so that numbers can be repeated. If another author breaks in and tries to steal these ideas, what is the probability that he or she will get the correct combination on the first attempt? Assume that the numbers are randomly selected. Given the number of possibilities, does it seem feasible to try opening the safe by making random guesses for the combination?

Short Answer

Expert verified

The probability that the correct combination is guessed on the first attempt is equal to 1100000000.

As the total number of different possibilities is extremely large, it is not feasible to guess the correct combination of numbers on the first try.

Step by step solution

01

Given information

A safe has a code consisting of four numbers selected from 0 to 99 with repetition.

02

Counting principle

The counting principle suggests that the number of possibilities for an event to occur iscounted at each step and then multiplied to get the total number of possibilities for that event to happen.

03

Calculation

Let A be the event of getting the correct combination of numbers.

The number of digits from 0 to 99 is equal to 100.

The total number of ways in which four numbers can be selected from 0 to 99 with repetition is shown below:

Totalnumberofways=100100100100=100000000

The number of ways of arranging the four numbers to get the correct combination is equal to 1.

The probability of guessing the correct combination of numbers is shown below:

PA=1100000000

Therefore, the probability of guessing the correct combination of numbers is equal to 1100000000.

Since theprobability value is extremely low(approximately equal to 0), it can be said it is not feasible to guess the correct combination of numbers on the first try.

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Most popular questions from this chapter

Probability from a Sample Space. In Exercises 33鈥36, use the given sample space or construct the required sample space to find the indicated probability.

Three Children Use this sample space listing the eight simple events that are possible when a couple has three children (as in Example 2 on page 135): {bbb, bbg, bgb, bgg, gbb, gbg, ggb, ggg}. Assume that boys and girls are equally likely, so that the eight simple events are equally likely. Find the probability that when a couple has three children, there is exactly one girl.

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Negative Test Result

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Subject Uses Drugs

45 (True Positive)

5 (False Negative)

Subject Does Not Use drugs

25 (False Positive)

480 (True Negative)

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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 奥别苍诲测鈥檚 or an order that is not accurate.

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 accurate.

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 13鈥20, express the indicated degree of likelihood as a probability value between 0 and 1.

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