/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q13 In Exercises 5鈥36, express all... [FREE SOLUTION] | 91影视

91影视

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.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Sample for a Poll There are 15,524,971 adults in Florida. If The Gallup organization randomly selects 1068 adults without replacement, are the selections independent or dependent? If the selections are dependent, can they be treated as being independent for the purposes of calculations?

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

Mega Millions As of this writing, the Mega Millions lottery is run in 44 states. Winning the jackpot requires that you select the correct five different numbers between 1 and 75 and, in a separate drawing, you must also select the correct single number between 1 and 15. Find the probability of winning the jackpot. How does the result compare to the probability of being struck by lightning in a year, which the National Weather Service estimates to be 1/960,000?

In Exercises 21鈥24, use these results from the 鈥1-Panel-THC鈥 test for marijuana use, which is provided by the company Drug Test Success: Among 143 subjects with positive test results, there are 24 false positive results; among 157 negative results, there are 3 false negative results. (Hint: Construct a table similar to Table 4-1, which is included with the Chapter Problem.)

Testing for Marijuana Use

a. How many subjects are included in the study?

b. How many of the subjects had a true negative result?

c. What is the probability that a randomly selected subject had a true negative result?

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

Social Security Numbers A Social Security number consists of nine digits in a particular order, and repetition of digits is allowed. After seeing the last four digits printed on a receipt, if you randomly select the other digits, what is the probability of getting the correct Social Security number of the person who was given the receipt?

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.

Four Children Using the same sample space and assumption from Exercise 35, find the probability that when a couple has four children, all four are of the same gender.

See all solutions

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.