/*! 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} Q3-56E Two fair coins are tossed, and t... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Q3-56E (page 193)

Two fair coins are tossed, and the following events are defined:

A: [Observe one head and one tail.]

B: [Observe at least one head.]

a. Define the possible sample points and assign probabilities to each.

b. Draw a Venn diagram for the experiment, showing the sample points and events A and B.

c. Find P(A), P(B) andP(A鈭�B).

d. Use the formula for conditional probability to find P (A/B)and P (B/A). Verify your answer by inspecting the Venn diagram and using the concept of reduced sample spaces.

Short Answer

Expert verified

Answer

  1. P (A)= [(H, T), (T, H)],P (B)= [(H, H), (H, T), (T, H)]
  2. Fig.1 Venn diagram
  3. 0.5, 0.75 & 0.5
  4. 0.67, 1.

Step by step solution

01

Step-by-Step SolutionStep 1: Identify the sample points

Probability is the study of prior records or the quantity and kind of probable outcomes to predict an event's result.

Sample points =[(H, H), (H, T), (T, H), (T, T)]P (A)= [(H, T), (T, H)]P (B)= [(H, H), (H, T), (T, H)]

02

Draw a Venn diagram

Here are all the sample points and events of A and B.

03

Find the required probability

P (A) =24=12= 0.5

P (B) =34= 0.75

P (A鈭�B) =24=12= 0.5

Hence, the required probabilities are 0.5, 0.75 & 0.5.

04

Find the required probability

P (A/B) =P (A鈭�B)P (B)=0.500.75= 0.67

P (B/A) =P (A鈭�B)P (A)=0.500.50= 1

Hence, the required probabilities are 0.67, 1.

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

Simulate the experiment described in Exercise 3.7 using any five identically shaped objects, two of which are one colour and the three another colour. Mix the objects, draw two, record the results, and then replace the objects. Repeat the experiment a large number of times (at least 100). Calculate the proportion of time events A, B, and C occur. How do these proportions compare with the probabilities you calculated in Exercise 3.7? Should these proportions equal the probabilities? Explain.

The diagram below describes the sample space of a particular experiment and events A and B .

  1. What is this type of diagram called?
  2. Suppose the sample points are equally likely. Find PAand PB.
  3. Suppose P1=P2=P3=P4=116and P5=P6=P7=P8=P9=P10=18 . Find PAand PB.

Suppose the events B1and B2are mutually exclusive and complementary events, such thatP(B1)=.75andP(B2)=.25 Consider another event A such that role="math" localid="1658212959871" P(AB1)=.3, role="math" localid="1658213029408" P(AB2)=.5.

  1. FindP(B1鈭�A).
  2. FindP(B2鈭�A)
  3. Find P(A) using part a and b.
  4. Findrole="math" localid="1658213127512" P(B1A).
  5. Findrole="math" localid="1658213164846" P(B2A).

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?

Characteristics of a new product. The long-run success of a business depends on its ability to market products with superior characteristics that maximize consumer satisfaction and that give the firm a competitive advantage (Kotler & Keller, Marketing Management, 2015). Ten new products have been developed by a food-products firm. Market research has indicated that the 10 products have the characteristics described by the following Venn diagram:

  1. Write the event that a product possesses all the desired characteristics as an intersection of the events defined in the Venn diagram. Which products are contained in this intersection?
  2. If one of the 10 products were selected at random to be marketed, what is the probability that it would possess all the desired characteristics?
  3. Write the event that the randomly selected product would give the firm a competitive advantage or would satisfy consumers as a union of the events defined in the Venn diagram. Find the probability of this union.
  4. Write the event that the randomly selected product would possess superior product characteristics and satisfy consumers. Find the probability of this intersection.
  5. Two of the 10 products will be selected for an ad campaign. How many different pairs of products are possible?
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Applied Mathematics

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

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.