Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 3: 1 (page 167)

An experiment results in one of the following sample points: E1,E2,E3 orE4 . Find PE4for each of the following cases.

  1. PE1=0.1,PE2=0.2,PE3=0.3
  2. PE1=PE2=PE3=PE4
  3. PE1=PE2=0.1andPE3=PE4

Short Answer

Expert verified
  1. PE4=0.4
  2. PE4=0.25
  3. PE4=0.4

Step by step solution

01

Finding the Probability of the event E4  where  PE1=0.1,PE2=0.2,PE3=0.3

The probability of all the sample points within a sample space is equal to ∑Pi=1

Given PE1=0.1,PE2=0.2,PE3=0.3

PE1+PE2+PE3+PE4=10.1+0.2+0.3+PE4=1PE4=1-0.1+0.2+0.3PE4=0.4

The probability of observing the event E4 is 0.4.

02

Finding the probability of the event E4  where PE1 = PE2 = PE3 = PE4

The probability of all the sample points within a sample space is equal to ∑Pi=1.

Given,

PE1=PE2=PE3=PE4

PE1+PE2+PE3+PE4=14×PE4=1PE4=14PE4=0.25

The probability of observing event E4 is0.25 .

03

Finding the probability of the event E4  where PE1=PE2=0.1  and  PE3=PE4

The probability of all the sample points within a sample space is equal to ∑Pi=1.

Given,

PE1=PE2=0.1and PE3=PE4

PE1+PE2+PE4=10.1+0.1+2×PE4=12×PE4=1-0.1+0.1PE4=0.4

The probability of observing the event E4 is 0.4 .

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

Drug testing in athletes.When Olympic athletes are tested for illegal drug use (i.e., doping), the results of a single positive test are used to ban the athlete from competition. Chance(Spring 2004) demonstrated the application of Bayes’s Rule for making inferences about testosterone abuse among Olympic athletes using the following example: In a population of 1,000 athletes, suppose 100 are illegally using testosterone. Of the users, suppose 50 would test positive for testosterone. Of the nonusers, suppose 9 would test positive.

  1. Given that the athlete is a user, find the probability that a drug test for testosterone will yield a positive result. (This probability represents the sensitivity of the drug test.)
  2. Given the athlete is a nonuser, find the probability that a drug test for testosterone will yield a negative result. (This probability represents the specificityof the drug test.)
  3. If an athlete tests positive for testosterone, use Bayes’s Rule to find the probability that the athlete is really doping. (This probability represents the positive predictive value of the drug test.)

Guilt in decision making.Refer to the Journal of Behavioral Decision Making(January 2007) study of theeffect of guilt emotion on how a decision maker focuseson a problem, Exercise 3.48 (p. 183). The results (numberresponding in each category) for the 171 study participantsare reproduced in the table below. Suppose one of the 171participants is selected at random.

Emotional

State

Choose

Stated Option

Do Not Choose

Stated Option

Totals

Guilt

Anger

Neutral

45

8

7

12

50

49

57

58

56

Totals

60

111

171

a.Given that the respondent is assigned to the guilty state, what is the probability that the respondent chooses the stated option?

b.If the respondent does not choose to repair the car, what is the probability that the respondent is in the anger state?

c.Are the events {repair the car} and {guilty state }
independent?

In a random sample of 106 social (or service) robots designed to entertain, educate, and care for human users, 63 were built with legs only, 20 with wheels only, 8 with both legs and wheels, and 15 with neither legs nor wheels. One of the 106 social robots is randomly selected and the design (e.g., wheels only) is noted.

  1. List the sample points for this study.
  2. Assign reasonable probabilities to the sample points.
  3. What is the probability that the selected robot is designed with wheels?
  4. What is the probability that the selected robot is designed with legs?

Wine quality and soil.The Journal of Wine Research(Vol.21, 2010) published a study of the effects of soil and climate on the quality of wine produced in Spain. The soil at two vineyards— Llarga and Solar—was the focus of the analysis.Wine produced from grapes grown in each of the two vineyards

was evaluated for each of three different years (growing seasons) by a wine-tasting panel. Based on the taste tests, the panel (as a group) selected the wine with the highest quality.

a.How many different wines were evaluated by the panel, where one wine was produced for each vineyard/growing season combination?

b.If the wines were all of equal quality, what is the probability that the panel selected a Llarga wine as the wine with the highest quality?

c.If the wines were all of equal quality, what is the probability that the panel selected a wine produced in year 3 as the wine with the highest quality?

d.The panel consisted of four different wine tasters who performed the evaluations independently of each other. If the wines were all of equal quality, what is the probability that all four tasters selected a Llarga wine as the wine with the highest quality?

Random shuffling of songs on Spotify. Spotify is a music streaming service that offers both free and subscription options. Users can create playlists and choose to use Spotify’s random shuffling feature to play back the songs. When the shuffling feature was first introduced, many users complained that the algorithm was not working. For example, in a playlist consisting of 2 songs by The White Stripes, 2 by Adele, and 1 by Maroon Five, two possible random orderings of the songs are:

A = {Adele 1, Adele 2, White Stripes 1, White Stripes 2, Maroon Five}

B = {Adele 2, White Stripes 1, Maroon Five, White Stripes 2, Adele 1}

  1. Find the probability that Adele 1 is selected as the first song to play from the playlist.
  2. Given that Adele 1 is selected as the first song, what is the probability that Adele 2 is selected as the second song to play from the playlist?
  3. Given that Adele 1 and Adele 2 are the first two songs selected, what is the probability that White Stripes 1 is selected as the third song to play from the playlist?
  4. Given that Adele 1, Adele 2, and White Stripes 1 are the first three songs selected, what is the probability that White Stripes 2 is selected as the fourth song to play from the playlist?
  5. Given that Adele 1, Adele 2, White Stripes 1 and White Stripes 2 are the first four songs selected, what is the probability that Maroon Five is selected as the last song to play from the playlist?
  6. Find the probability of List A by multiplying the probabilities in parts a–e.
  7. Many users considered List B to be random, but not List A. Demonstrate that the probability of List B is the same as the probability of List A. [Note: In response to user complaints, Spotify now uses a different random shuffling algorithm, one that prevents an outcome like List A from occurring.]
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Applied Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Geometry

Read Explanation

Mechanics Maths

Read Explanation

Calculus

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