/*! 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 137 The following information reflec... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 137

The following information reflects the results of a survey reported by Mya Frazier in an \(A d\) Age Insights white paper. \({ }^{11}\) Working spouses were asked "Who is the household breadwinner?" Suppose that one person is selected at random from these 200 individuals. $$\begin{array}{lcccc} & \multicolumn{3}{c} {\text { Spouse or }} \\\& \text { You } & \text { Significant Other } & \text { About Equal } & \text { Totals } \\\\\hline \text { Men } & 64 & 16 & 20 & 100 \\\\\text { Women } & 32 & 45 & 23 & 100 \\\\\hline \text { Totals } & 96 & 61 & 43 & 200\end{array}$$ a. What is the probability that this person will identify his/herself as the household breadwinner? b. What is the probability that the person selected will be a man who indicates that he and his spouse/significant other are equal breadwinners? c. If the person selected indicates that the spouse or significant other is the breadwinner, what is the probability that the person is a man?

Short Answer

Expert verified
Based on the survey results: a. The probability that a randomly selected person will identify themselves as the household breadwinner is 0.48 or 48%. b. The probability that a randomly selected person will be a man who indicates that he and his spouse/significant other are equal breadwinners is 0.1 or 10%. c. If a randomly selected person indicates that the spouse or significant other is the breadwinner, the probability that the person is a man is approximately 0.2623 or 26.23%.

Step by step solution

01

Part (a)

We need to calculate the probability that a randomly selected person will identify themselves as a the breadwinner. This will be determined by dividing the number of people who identified themselves as the breadwinner (men and women) by the total number of people surveyed. So, the probability is given by: P(Self breadwinner) = (Number of men who identified themselves as breadwinners + Number of women who identified themselves as breadwinners) / Total number of people surveyed P(Self breadwinner) = (64 (men) + 32 (women)) / 200 P(Self breadwinner) = 96 / 200 P(Self breadwinner) = 0.48
02

Part (b)

Now, we need to calculate the probability that a randomly selected person will be a man who indicates that he and his spouse/significant other are equal breadwinners. This will be determined by dividing the number of men indicating equal breadwinners (20) by the total number of people surveyed (200). So, the probability is given by: P(Man indicating equal breadwinners) = Number of men indicating equal breadwinners / Total number of people surveyed P(Man indicating equal breadwinners) = 20 / 200 P(Man indicating equal breadwinners) = 0.1
03

Part (c)

Lastly, we need to find the probability that a person is a man if the person selected indicates that the spouse or significant other is the breadwinner. We can use the conditional probability formula: P(Man | Spouse breadwinner) = P(Man and Spouse breadwinner) / P(Spouse breadwinner) We first need to calculate the probabilities P(Man and Spouse breadwinner) and P(Spouse breadwinner). P(Man and Spouse breadwinner) = Number of men indicating spouse breadwinner / Total number of people surveyed P(Man and Spouse breadwinner) = 16 / 200 P(Man and Spouse breadwinner) = 0.08 P(Spouse breadwinner) = (Number of men indicating spouse breadwinner + Number of women indicating spouse breadwinner) / Total number of people surveyed P(Spouse breadwinner) = (16 (men) + 45 (women)) / 200 P(Spouse breadwinner) = 61 / 200 P(Spouse breadwinner) = 0.305 Now, we can calculate the conditional probability: P(Man | Spouse breadwinner) = P(Man and Spouse breadwinner) / P(Spouse breadwinner) P(Man | Spouse breadwinner) = 0.08 / 0.305 P(Man | Spouse breadwinner) 鈮� 0.2623 In conclusion: a. The probability that a person will identify themselves as the household breadwinner is 0.48. b. The probability that a person selected will be a man who indicates that he and his spouse/significant other are equal breadwinners is 0.1. c. If the person selected indicates that the spouse or significant other is the breadwinner, the probability that the person is a man is approximately 0.2623.

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!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Conditional Probability
Conditional probability helps us understand the likelihood of an event happening, given that another event has already occurred. It's a crucial concept in probability, especially when dealing with dependent events. For instance, in the given problem, if a person indicates that their spouse or significant other is the breadwinner, we want to find the probability that this person is a man. To solve this, we use the conditional probability formula:
  • \( P(A | B) = \frac{P(A \text{ and } B)}{P(B)} \)
  • Here, \( P(A | B) \) is the probability of event \( A \) occurring given that \( B \) has occurred.
In our scenario, event \( A \) is that the person is a man, and event \( B \) is that the spouse/significant other is identified as the breadwinner. Using the provided data, we calculate these probabilities and find that the conditional probability for a man, given that the spouse is the breadwinner, is approximately 0.2623.
Survey Sampling
Survey sampling is a method used to collect data from a subset of a population in order to make inferences about the entire population. In the problem at hand, 200 working spouses were surveyed about the primary breadwinner in the household. This sample size is critical because it affects the reliability of the conclusions drawn.
Sampling involves random selection which ensures that every member of the population has an equal chance of being selected. This helps avoid bias and makes the survey results more generalizable to the broader population.
The total sample collected for this survey is well-balanced between men and women, each representing half of the 200 respondents surveyed. This balance allows for a straightforward analysis of gender roles in terms of breadwinners, aligning well with equal representation goals in statistical analysis.
Probability Calculation
Probability calculation is a foundational part of statistics that allows us to measure the likelihood of an event. It's often expressed as a number between 0 and 1, where 0 means the event will not occur, and 1 means it will certainly occur. In this survey, we have several probabilities to calculate.

Self-identified Breadwinner Probability

First, to find the probability that a randomly selected person identifies themselves as the breadwinner, the number of such responses (96) is divided by the total sample size (200), yielding a probability of 0.48.

Equal Breadwinner Probability

For a man indicating he and his partner are equal, the relevant data point is 20 out of 200 respondents, resulting in a probability of 0.1.
These calculations are crucial for interpreting survey data and making informed decisions about societal trends in household dynamics.
Equal Breadwinners Analysis
The concept of equal breadwinners refers to households where both partners perceive their contributions as equal. This scenario is growing increasingly common in modern households, as evidenced by the survey results.

Men's Perspective

In our survey, 20 men reported that they and their partners were equal in financial contributions. This represents 20% of all male respondents surveyed.

Women's Perspective

Similarly, 23 women reported equality in breadwinning, making up 23% of female respondents.
Analyzing these responses provides insights into changes in societal norms and gender roles. It suggests a shift towards more gender-balanced financial roles within households, reflecting broader economic and social changes.

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

Two city council members are to be selected from a total of five to form a sub- committee to study the city's traffic problems. a. How many different subcommittees are possible? b. If all possible council members have an equal chance of being selected, what is the probability that members Smith and Jones are both selected?

A food company plans to conduct an experiment to compare its brand of tea with that of two competitors. A single person is hired to taste and rank each of three brands of tea, which are unmarked except for identifying symbols \(A, B\), and \(C\). a. Define the experiment. b. List the simple events in \(S\). c. If the taster has no ability to distinguish a difference in taste among teas, what is the probability that the taster will rank tea type \(A\) as the most desirable? As the least desirable?

A shipping container contains seven complex electronic systems. Unknown to the purchaser, three are defective. Two of the seven are selected for thorough testing and are then classified as defective or nondefective. What is the probability that no defectives are found?

If an experiment is conducted, one and only one of three mutually exclusive events \(S_{1}, S_{2},\) and \(S_{3}\) can occur, with these probabilities: $$P\left(S_{1}\right)=.2 \quad P\left(S_{2}\right)=.5 \quad P\left(S_{3}\right)=.3$$ The probabilities of a fourth event \(A\) occurring, given that event \(S_{1}, S_{2},\) or \(S_{3}\) occurs, are $$P\left(A \mid S_{1}\right)=.2 \quad P\left(A \mid S_{2}\right)=.1 \quad P\left(A \mid S_{3}\right)=.3$$ If event \(A\) is observed, find \(P\left(S_{1} \mid A\right), P\left(S_{2} \mid A\right),\) and \(P\left(S_{3} \mid A\right)\).

Although there is legal protection for "whistle blowers" - employees who report illegal or unethical activities in the workplace- it has been reported that approximately \(23 \%\) of those who reported fraud suffered reprisals such as demotion or poor performance ratings. Suppose the probability that an employee will fail to report a case of fraud is .69. Find the probability that an employee who observes a case of fraud will report it and will subsequently suffer some form of reprisal.
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Decision Maths

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Pure Maths

Read Explanation

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.