/*! 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 17 In a survey of 500 randomly sele... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 17

In a survey of 500 randomly selected Americans, it was determined that 22 play soccer. What is the probability that a randomly selected American plays soccer?

Short Answer

Expert verified
The probability is 0.044 or 4.4%.

Step by step solution

01

Identify Given Values

There are two key pieces of information provided in the problem: the total number of people surveyed and the number of people who play soccer. The total number of people surveyed is 500, and the number of people who play soccer is 22.
02

Write Down the Probability Formula

The formula for probability is given by the number of favorable outcomes divided by the total number of possible outcomes. Mathematically, this can be written as: \[P(A) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}\]
03

Substitute Given Values into the Formula

Substitute the given values into the probability formula:\[P(\text{plays soccer}) = \frac{22}{500}\]
04

Simplify the Fraction

To find the probability, divide 22 by 500:\[P(\text{plays soccer}) = \frac{22}{500} = 0.044\]
05

Interpret the Result

The result 0.044 means that there is a 4.4% chance that a randomly selected American plays soccer.

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.

Favorable Outcomes
In probability, 'favorable outcomes' refer to the specific events we are interested in. In our exercise, we want to find the probability a randomly selected American plays soccer. The favorable outcome is the number of people who play soccer among the surveyed group. Here, out of 500 surveyed people, 22 play soccer. So, 22 is our favorable outcome. This allows us to focus only on occurrences that meet our criteria.
We must keep it clear that favorable outcomes are not always positive events but those we want to measure or observe.
Total Outcomes
Total outcomes in probability represent all possible outcomes in a given scenario. In our example, the total outcomes are the 500 people surveyed. The total number of outcomes provides the base for calculating probabilities.
When considering total outcomes, it鈥檚 crucial to understand that we include all cases, whether they meet our criteria or not. This forms the denominator in our probability formula and allows us to make proportional comparisons.
Probability Formula
The probability formula is a fundamental tool in statistics. It is given by:
equation \[ P(A) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} \]
This formula helps us calculate the likelihood of an event occurring. In our survey example, we are interested in the probability that a randomly selected American plays soccer. Here, A represents the event of playing soccer.
By substituting the number of favorable outcomes (22) and the total outcomes (500), we compute this probability.
Simplifying Fractions
After substituting the values into the probability formula, we often get a fraction. In our example:
equation \[ P(\text{plays soccer}) = \frac{22}{500} \]
This fraction can be simplified if possible. Although in this case, 22 and 500 don't share common factors, so it simplifies to approximately:
equation \[ P(\text{plays soccer}) = 0.044 \]
Simplifying fractions or converting them to decimals makes the probability easier to interpret.
Interpreting Results
Interpreting probability results is the final step. It involves understanding the implications of the calculated probability. In our example, after simplifying, we find that \[ P(\text{plays soccer}) = 0.044 \]
This means there is a 4.4% chance that a randomly selected American from the surveyed group plays soccer.
Interpretation in percent form often makes it easier for people to understand relationships and chances in real-world scenarios. Here, it helps us grasp that while soccer is not extremely popular, it still has a noticeable prevalence.

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

A committee consisting of four women and three men will randomly select two people to attend a conference in Hawaii. Find the probability that both are women.

In a recent Harris Poll, a random sample of adult Americans (18 years and older) was asked, "When you see an ad emphasizing that a product is 'Made in America,' are you more likely to buy it, less likely to buy it, or neither more nor less likely to buy it?" The results of the survey, by age group, are presented in the following contingency table. $$ \begin{array}{lrrrrr} & \mathbf{1 8 - 3 4} & \mathbf{3 5 - 4 4} & \mathbf{4 5 - 5 4} & \mathbf{5 5 +} & \text { Total } \\ \hline \text { More likely } & 238 & 329 & 360 & 402 & \mathbf{1 3 2 9} \\ \hline \text { Less likely } & 22 & 6 & 22 & 16 & \mathbf{6 6} \\ \hline \begin{array}{l} \text { Neither more } \\ \text { nor less likely } \end{array} & 282 & 201 & 164 & 118 & \mathbf{7 6 5} \\ \hline \text { Total } & \mathbf{5 4 2} & \mathbf{5 3 6} & \mathbf{5 4 6} & \mathbf{5 3 6} & \mathbf{2 1 6 0} \end{array} $$ (a) What is the probability that a randomly selected individual is 35-44 years of age, given the individual is more likely to buy a product emphasized as "Made in America"? (b) What is the probability that a randomly selected individual is more likely to buy a product emphasized as "Made in America," given the individual is \(35-44\) years of age? (c) Are 18 - to 34 -year-olds more likely to buy a product emphasized as "Made in America" than individuals in general?

Suppose that a computer chip company has just shipped 10,000 computer chips to a computer company. Unfortunately, 50 of the chips are defective. (a) Compute the probability that two randomly selected chips are defective using conditional probability. (b) There are 50 defective chips out of 10,000 shipped. The probability that the first chip randomly selected is defective is \(\frac{50}{10,000}=0.005 .\) Compute the probability that two randomly selected chips are defective under the assumption of independent events. Compare your results to part (a). Conclude that, when small samples are taken from large populations without replacement, the assumption of independence does not significantly affect the probability.

In 2002, Valerie Wilson won \(\$ 1\) million in a scratch-off game (Cool Million) from the New York lottery. Four years later, she won \(\$ 1\) million in another scratch-off game \((\$ 3,000,000\) Jubilee \(),\) becoming the first person in New York state lottery history to win \(\$ 1\) million or more in a scratch-off game twice. In the first game, she beat odds of 1 in 5.2 million to win. In the second, she beat odds of 1 in 705,600 . (a) What is the probability that an individual would win \(\$ 1\) million in both games if they bought one scratch-off ticket from each game? (b) What is the probability that an individual would win \(\$ 1\) million twice in the \(\$ 3,000,000\) Jubilee scratch-off game?

For a parallel structure of identical components, the system can succeed if at least one of the components succeeds. Assume that components fail independently of each other and that each component has a 0.15 probability of failure. (a) Would it be unusual to observe one component fail? Two components? (b) What is the probability that a parallel structure with 2 identical components will succeed? (c) How many components would be needed in the structure so that the probability the system will succeed is greater than \(0.9999 ?\)
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Pure Maths

Read Explanation

Logic and Functions

Read Explanation

Decision Maths

Read Explanation

Applied Mathematics

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.