Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 3: Q3.12 (page 187)

Mark is deciding which route to take to work. His choices are I = the Interstate and F = Fifth Street.

•P(I)=0.44andP(F)=0.56

• role="math" localid="1652098516712" P(I∩F)=0because Mark will take only one route to work.

What is the probability of P(IORF)?

Short Answer

Expert verified

P(IorF)=1

Step by step solution

01

Basic Concept

Probability is the likelihood of an event.

As per probability rule,

P(AUB)=P(A)+P(B)-P(A∩B)

02

Explanation 

It is given that Mark takes Interstate or fifth street route to work, withPr(I)andPr(F)=0.44and0.56 respectively.

As he can take only one route & both routes can never be taken together, so these events are mutually exclusive, represented by disjoint sets whose intersection i.e.P(I&F)=P(I∩F)=0

So,P(IorF)=P(IUF)=P(I)+P(F)-P(I∩F)

P(IorF)=0.44+0.56=1

This shows - it is certain that Mark will take either route to work

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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

What is the sum of the probabilities of an event and its complement?

Use the following information to answer the next four exercises. Table 3.15 shows a random sample of musicians and how they learned to play their instruments

Find P(musician is a male AND had private instruction).

Use the The graph shown is based on more than170,000interviews done by Gallup that took place from January through December 2012. The sample consists of employed Americans 18 years of age or older. The Emotional Health Index Scores are the sample space. We randomly sample one Emotional Health Index Score.

Find the probability that an Emotional Health Index Score is 82.7

Approximately 281,000,000people over age five live in the United States. Of these people, 55,000,000speak a language other than English at home. Of those who speak another language at home, 62.3%speak Spanish.

Let:E = speaks English at home; E′ = speaks another language at home; S = speaks Spanish;

Finish each probability statement by matching the correct answer.

The following table of data obtained from www.baseball-almanac.com shows hit information for four players. Suppose that one hit from the table is randomly selected.

Are "the hit being made by Hank Aaron" and "the hit being a double" independent events?

a. Yes, because P(hit by Hank Aaron | hit is a double) =P(hit by Hank Aaron)

b. No, because P(hit by Hank Aaron | hit is a double) ≠P(hit is a double)

c. No, because P(hit is by Hank Aaron | hit is a double) ≠P(hit by Hank Aaron)

d. Yes, because P(hit is by Hank Aaron | hit is a double) =P(hit is a double)
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation

Logic and Functions

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.

Sign-up for free