/*! 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} Problem 19 Explain why the statement is inc... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 19

Explain why the statement is incorrect. A red die and a green die are tossed. The probability that a 6 will appear uppermost on the red die is \(\frac{1}{6}\), and the probability that a 1 will appear uppermost on the green die is \(\frac{1}{6}\). Hence, the probability that the red die will show a 6 or the green die will show a 1 is \(\frac{1}{6}+\frac{1}{6}\).

Short Answer

Expert verified
The original statement is actually correct because the events of the red die showing a 6 and the green die showing a 1 are independent. Therefore, the probability of either event occurring is the sum of their individual probabilities: P(A 鈭� B) = P(A) + P(B) = \(\frac{1}{6} + \frac{1}{6} = \frac{2}{6} = \frac{1}{3}\).

Step by step solution

01

Define the events and probabilities

Let A be the event that the red die shows a 6, and B be the event that the green die shows a 1. The probability of A (P(A)) is given as \(\frac{1}{6}\), and the probability of B (P(B)) is given as \(\frac{1}{6}\).
02

Determine if the events are independent

Two events are independent if the occurrence of one event does not affect the occurrence of the other event. Since the outcomes of rolling the red and green dice are not related in any way, we can conclude that the events A and B are independent.
03

Calculate the probability of either event occurring

Since the events are indeed independent, the probability of either A or B occurring (A 6 on the red die or a 1 on the green die) is the sum of their individual probabilities. Therefore, the probability of either event occurring is: P(A 鈭� B) = P(A) + P(B) = \(\frac{1}{6} + \frac{1}{6} = \frac{2}{6} = \frac{1}{3}\). The original statement is thus correct. The probability of the red die showing a 6 or the green die showing a 1 is indeed \(\frac{1}{6}+\frac{1}{6}\).

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

A study of the faculty at U.S. medical schools in 2006 revealed that \(32 \%\) of the faculty were women and \(68 \%\) were men. Of the female faculty, \(31 \%\) were full/ associate professors, \(47 \%\) were assistant professors, and \(22 \%\) were instructors. Of the male faculty, \(51 \%\) were full/associate professors, \(37 \%\) were assistant professors, and \(12 \%\) were instructors. If a faculty member at a U.S. medical school selected at random holds the rank of full/associate professor, what is the probability that she is female?

What is the probability that at least two of the nine justices of the U.S. Supreme Court have the same birthday?

CAR THEFT Figures obtained from a city's police department seem to indicate that, of all motor vehicles reported as stolen, \(64 \%\) were stolen by professionals whereas \(36 \%\) were stolen by amateurs (primarily for joy rides). Of those vehicles presumed stolen by professionals, \(24 \%\) were recovered within \(48 \mathrm{hr}, 16 \%\) were recovered after \(48 \mathrm{hr}\), and \(60 \%\) were never recovered. Of those vehicles presumed stolen by amateurs, \(38 \%\) were recovered within \(48 \mathrm{hr}, 58 \%\) were recovered after \(48 \mathrm{hr}\), and \(4 \%\) were never recovered. a. Draw a tree diagram representing these data. b. What is the probability that a vehicle stolen by a professional in this city will be recovered within \(48 \mathrm{hr}\) ? c. What is the probability that a vehicle stolen in this city will never be recovered?

There are 12 signs of the Zodiac: Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricom, Aquarius, and Pisces. Each sign corresponds to a different calendar period of approximately 1 month. Assuming that a person is just as likely to be born under one sign as another, what is the probability that in a group of five people at least two of them a. Have the same sign?

Quaurr CoNrroL. An automobile manufacturer obtains the microprocessors used to regulate fuel consumption in its automobiles from three microelectronic firms: \(\mathrm{A}, \mathrm{B}\), and C. The quality-control department of the company has determined that \(1 \%\) of the microprocessors produced by firm \(A\) are defective, \(2 \%\) of those produced by firm \(B\) are defective, and \(1.5 \%\) of those produced by firm \(\mathrm{C}\) are defective. Firms \(\mathrm{A}, \mathrm{B}\), and \(\mathrm{C}\) supply \(45 \%, 25 \%\), and \(30 \%\), respectively, of the microprocessors used by the company. What is the probability that a randomly selected automobile manufactured by the company will have a defective microprocessor?
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Geometry

Read Explanation

Decision Maths

Read Explanation

Probability and Statistics

Read Explanation

Pure Maths

Read Explanation

Discrete Mathematics

Read Explanation
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.