/*! 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 34 A sample of 500 large companies ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 34

A sample of 500 large companies showed that 120 of them offer free psychiatric help to their employees who suffer from psychological problems. If one company is selected at random from this sample, what is the probability that this company offers free psychiatric help to its employees who suffer from psychological problems? What is the probability that this company does not offer free psychiatric help to its employees who suffer from psychological problems? Do these two probabilities add up to \(1.0\) ? If yes, why?

Short Answer

Expert verified
The probability that a randomly selected company offers free psychiatric help is \(0.24\) or \(24\%\). The probability that it does not offer free psychiatric help is \(0.76\) or \(76\%\). And yes, these two probabilities do indeed add up to \(1.0\), since a company either offers or does not offer free psychiatric help, it covers all the possibilities.

Step by step solution

01

Calculate the Probability of Offering Free Help

To calculate the probability of offering free psychiatric help \(P(F)\), divide the number of companies offering such help by the total number of companies in the sample. Here, \(P(F) = 120 / 500 = 0.24\).
02

Calculate the Probability of Not Offering Free Help

To calculate the probability of not offering free psychiatric help \(P(NF)\), subtract the probability of a company offering free help from 1. Alternatively, it can be directly computed by taking the ratio of companies not offering free help to total companies. In this case, \(P(NF) = 1 - P(F) = 1 - 0.24 = 0.76\) or \(P(NF) = (500 - 120) / 500 = 0.76\).
03

Do the Probabilities Add Up

To confirm if \(P(F) + P(NF) = 1.0\), simply add the two obtained probabilities i.e. \(0.24 + 0.76 = 1.0\). This makes sense as it confirms to the rule of probability that for any sample space, the sum of the probabilities of all its individual outcomes always equals to one. This is because any given company either offers free psychiatric help or does not, covering all the possibilities.

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.

Psychiatric Help
Psychiatric help is crucial for maintaining employees' mental health at work. In this context, some companies offer free psychiatric help to employees suffering from psychological issues. Providing such help can significantly boost employee well-being and productivity. This type of support is part of an organization's commitment to fostering a healthy workplace environment.
Understanding the importance of psychiatric help in companies helps us realize the role this plays in both employee satisfaction and retention.
Sample Size
Sample size refers to the number of observations or entities in a statistical sample. In this exercise, the sample size is 500, representing large companies.
When dealing with probability, the sample size is critical as it influences the reliability of the results. A larger sample size generally leads to more accurate and reliable results because it minimizes the effects of outliers and biases.
Conversely, a smaller sample might not accurately reflect the whole population, leading to skewed probabilities.
Probability Calculation
Probability calculation helps determine the likelihood of an event occurring within a sample. It's expressed as a number between 0 and 1. In this exercise, we're interested in finding out the probability that a company offers free psychiatric help.
To determine probability, divide the number of desired outcomes by the total number of possible outcomes. For our example, we calculate the probability of a company offering free help as follows:
  • Number of companies offering help: 120
  • Total companies in sample: 500

Thus, the probability calculation is: \[P(F) = \frac{120}{500} = 0.24\] This means there's a 24% chance you will pick a company that offers such help from this sample.
Complement Rule
The complement rule in probability states that the probability of an event not happening is equal to one minus the probability of the event happening. This concept is essential for calculating probabilities when interested in multiple outcomes.
In our scenario, knowing the probability of a company that does not offer psychiatric help streamlines calculations:
  • Probability of offering help: 0.24
  • Probability of not offering help: 1 - 0.24

Thus, the calculation becomes: \[P(NF) = 1 - P(F) = 0.76\]
This 76% probability assures us that all possible outcomes (offering help or not) total up to 1, aligning with the fundamental principle of probability.

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

Many states have a lottery game, usually called a Pick-4, in which you pick a four-digit number such as 7359 . During the lottery drawing, there are four bins, each containing balls numbered 0 through 9\. One ball is drawn from each bin to form the four-digit winning number. a. You purchase one ticket with one four-digit number. What is the probability that you will win this lottery game? b. There are many variations of this game. The primary variation allows you to win if the four digits in your number are selected in any order as long as they are the same four digits as obtained by the lottery agency. For example, if you pick four digits making the number 1265 , then you will win if \(1265,2615,5216,6521\), and so forth, are drawn. The variations of the lottery game depend on how many unique digits are in your number. Consider the following four different versions of this game. i. All four digits are unique (e.g., 1234 ) ii. Exactly one of the digits appears twice (e.g., 1223 or 9095 ) iii. Two digits each appear twice (e.g., 2121 or 5588 ) iv. One digit appears three times (e.g., 3335 or 2722 ) Find the probability that you will win this lottery in each of these four situations.

Given that \(A, B\), and \(C\) are three independent events, find their joint probability for the following. a. \(P(A)=.30, \quad P(B)=.50\), and \(P(C)=.70\) b. \(P(A)=.40, \quad P(B)=.50\), and \(P(C)=.60\)

Explain the meaning of the union of two events. Give one example.

The following table gives a two-way classification of all basketball players at a state university who began their college careers between 2004 and 2008 , based on gender and whether or not they graduated. $$ \begin{array}{lcc} \hline & \text { Graduated } & \text { Did Not Graduate } \\ \hline \text { Male } & 126 & 55 \\ \text { Female } & 133 & 32 \\ \hline \end{array} $$ a. If one of these players is selected at random, find the following probabilities. i. \(P\) (female and graduated) ii. \(P\) (male and did not graduate) b. Find \(P\) (graduated and did not graduate). Is this probability zero? If yes, why?

The probability that an employee at a company is a female is .36. The probability that an employee is a female and married is .19. Find the conditional probability that a randomly selected employee from this company is married given that she is a female.
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Discrete Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Geometry

Read Explanation

Pure Maths

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.