Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 3: Q35E (page 180)

The outcomes of two variables are (Low, Medium, High) and (On, Off), respectively. An experiment is conducted in which the outcomes of each of the two variables are observed. The accompanying two-way table gives the probabilities associated with each of the six possible outcome pairs.

Low

Medium

High

On

.50

.10

.05

Off

.25

.07

.03

Consider the following events:

A: {On}

B: {Medium or on}

C: {Off and Low}

D: {High}

a. Find P (A).

b. Find P (B).

c. Find P (C).

d. Find P (D).

e. FindP(AC).

f. FindP(A∪B).

g. FindP(A∩B).

h. Consider each pair of events (A and B, A and C, A and D, B and C, B and D, C and D). List the pairs of events that are mutually exclusive. Justify your choices.

Short Answer

Expert verified
  1. 0.65
  2. 0.72
  3. 0.25
  4. 0.08
  5. 0.35
  6. 0.72
  7. 0
  8. A and C, A and D, B and D, & C and D.

Step by step solution

01

Introduction

Probability is organizing trials and comparing the number of possible outcomes to the number of desired outcomes.

02

Find P (A)

P(A)=[0.50+0.10+0.05]=0.65

03

Find P (B)

P(B)=P(on)+P(medium)-P(medium∩low)=[(0.10+0.7)+(0.50+0.10+0.05)−0.10]=[0.17+0.65−0.10]=0.72

04

Find P (C)

P(C)=0.25

05

Find P (D)

P(D)=[0.05+0.03]=0.08

06

Find P(Ac)

P(Ac)=1−P(A)=1−0.65=0.35

07

Find

P(A∪B)=P[Onor(mediumorOn)]=P(Onormedium)=P(B)=0.72

08

Find

P(A∩C)=P[Onand(OffandLow)

Here, On & Off and Low are mutually exclusive.

P(A∩C)=0

09

List all the mutually exclusive pairs

P(A∩C)=0

P(A∩D)=0

P(B∩C)=0

P(C∩D)=0

Therefore,A and C, A and D, B and D, & C and Dare mutually exclusive pairs.

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

Inactive oil and gas structures. U.S. federal regulations require that operating companies clear all inactive offshore oil and gas structures within 1 year after production ceases. Researchers at the Louisiana State University Center for Energy Studies gathered data on both active and inactive oil and gas structures in the Gulf of Mexico (Oil & Gas Journal, Jan. 3, 2005). They discovered that the Gulf of Mexico has 2,175 active and 1,225 idle (inactive) structures. The following table breaks down these structures by type (caisson, well protector, or fixed platform). Consider the structure type and active status of one of these oil/gas structures.

Structure type

Caisson

Well protector

Fixed platform

Totals

Active

503

225

1447

2175

Inactive

598

177

450

1225

a. List the simple events for this experiment.

b. Assign reasonable probabilities to the simple events.

c. Find the probability that the structure is active.

d. Find the probability that the structure is a well protector.

e. Find the probability that the structure is an inactive caisson.

Working on summer vacation.Refer to the Harris Interactive(July 2013) poll of whether U.S. adults workduring summer vacation, Exercise 3.13 (p. 169). Recall thatthe poll found that 61% of the respondents work duringtheir summer vacation, 22% do not work at all while onvacation, and 17% were unemployed. Also, 38% of thosewho work while on vacation do so by monitoring theirbusiness emails.

a.Given that a randomly selected poll respondent will work while on summer vacation, what is the probability that the respondent will monitor business emails?

b.What is the probability that a randomly selected poll respondent will work while on summer vacation and will monitor business emails?

c.What is the probability that a randomly selected poll respondent will not work while on summer vacation and will monitor business emails?

World Cup soccer match draws. Every 4 years the world’s 32 best national soccer teams compete for the World Cup. Run by FIFA (Fédération Internationale de Football Association), national teams are placed into eight groups of four teams, with the group winners advancing to play for the World Cup. Chance(Spring 2007) investigated the fairness of the 2006 World Cup draw. Each of the top 8 seeded teams (teams ranked 1–8, called pot 1) were placed into one of the eight groups (named Group A, B, C, D, E, F, G, and H). The remaining 24 teams were assigned to 3 pots of 8 teams each to achieve the best possible geographic distribution between the groups. The teams in pot 2 were assigned to groups as follows: the first team drawn was placed into Group A, the second team drawn was placed in to Group B, etc. Teams in pots 3 and 4 were assigned to the groups in similar fashion. Because teams in pots 2–4 are not necessarily placed there based on their world ranking, this typically leads to a “group of death,” i.e., a group involving at least two highly seeded teams where only one can advance.

  1. In 2006, Germany (as the host country) was assigned as the top seed in Group A. What is the probability that Paraguay (with the highest ranking in pot 2) was assigned to Group A?
  2. Many soccer experts viewed the South American teams (Ecuador and Paraguay) as the most dangerous teams in pot 2. What is the probability one of the South American teams was assigned to Group A?
  3. In 2006, Group B was considered the “group of death,” with England (world rank 2), Paraguay (highest rank in pot 2), Sweden (2nd highest rank in pot 3), and Trinidad and Tobago. What is the probability that Group B included the team with the highest rank in pot 2 and the team with one of the top two ranks in pot 3?
  4. In drawing teams from pot 2, there was a notable exception in 2006. If a South American team (either Ecuador or Paraguay) was drawn into a group with another South American team, it was automatically moved to the next group. This rule impacted Group C (Argentina as the top seed) and Group F (Brazil as the top seed), because they already had South American teams, and groups that followed these groups in the draw. Now Group D included the eventual champion Italy as its top seed. What is the probability that Group D was not assigned one of the dangerous South American teams in pot 2?

Chance of an Avon sale.The probability that an Avon salesperson sells beauty products to a prospective customer on the first visit to the customer is .4. If the salesperson fails to make the sale on the first visit, the probability that the sale will be made on the second visit is .65. The salesperson never visits a prospective customer more than twice. What is the probability that the salesperson will make a sale to a particular customer?

Chance of winning at “craps.” A version of the dice game“craps” is played in the following manner. A player starts by rolling two balanced dice. If the roll (the sum of the two numbers showing on the dice) results in a 7 or 11, the player wins. If the roll results in a 2 or a 3 (called craps), the player loses. For any other roll outcome, the player continues to throw the dice until the original roll outcome recurs (in which case the player wins) or until a 7 occurs

(in which case the player loses).

a. What is the probability that a player wins the game on the first roll of the dice?

b. What is the probability that a player loses the game on the first roll of the dice?

c. If the player throws a total of 4 on the first roll, what is the probability that the game ends (win or lose) on the next roll?
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

Read Explanation

Pure Maths

Read Explanation

Calculus

Read Explanation

Probability and Statistics

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