/*! 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 13 About \(13 \%\) of the populatio... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 13

About \(13 \%\) of the population is left-handed. If two people are randomly selected, what is the probability that both are left-handed? What is the probability that at least one is right-handed?

Short Answer

Expert verified
The probability that both people are left-handed is 0.0169. The probability that at least one is right-handed is 0.9831.

Step by step solution

01

Determine the Probability of One Person Being Left-Handed

The probability that one person is left-handed is given as 13%, which can be written as a decimal: \( P(\text{Left-Handed}) = 0.13 \).
02

Calculate the Probability that Both People Are Left-Handed

To find the probability that both people are left-handed, multiply the probabilities for each person, assuming the events are independent:\[ P(\text{Both Left-Handed}) = 0.13 \times 0.13 = 0.0169 \].
03

Determine the Probability of One Person Being Right-Handed

The probability that one person is right-handed is the complement of the probability that the person is left-handed:\[ P(\text{Right-Handed}) = 1 - P(\text{Left-Handed}) = 1 - 0.13 = 0.87 \].
04

Calculate the Probability that at Least One Person is Right-Handed

To find the probability that at least one of the two people is right-handed, use the complement rule. First, find the probability that both are left-handed (from Step 2), then subtract this from 1:\[ P(\text{At Least One Right-Handed}) = 1 - P(\text{Both Left-Handed}) = 1 - 0.0169 = 0.9831 \].

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.

left-handed probability
Left-handedness is less common in the general population. Around 13% of people are left-handed. When we express this probability in decimal form, it becomes 0.13. This can help in various probability calculations. For example, knowing the chance of one person being left-handed is the starting point for more complex scenarios. Understanding basic probabilities like this is crucial for solving problems involving multiple events.
independent events
In probability, independent events mean the outcome of one event does not affect the outcome of another. If we consider two random people, the probability of each being left-handed is independent of the other. To find the probability that both individuals are left-handed, we multiply their individual probabilities: \[ P(\text{Both Left-Handed}) = P(\text{Left-Handed}) \times P(\text{Left-Handed}) = 0.13 \times 0.13 = 0.0169 \] Recognizing events as independent simplifies calculations and is essential in multi-step problems.
complement rule
The complement rule is a crucial concept in probability. It states that the probability of an event not occurring is 1 minus the probability of the event occurring. For example, if 13% of people are left-handed, then 87% are not. Expressed in probability terms:\[ P(\text{Right-Handed}) = 1 - P(\text{Left-Handed}) = 1 - 0.13 = 0.87 \] This rule helps find probabilities indirectly and is useful when calculating 'at least' probabilities, like the chance that at least one person in a group is right-handed.
probability of complementary events
Complementary events are pairs of outcomes where one must occur if the other does not. For instance, someone being left-handed or right-handed are complementary events. To find the probability that at least one of two people is right-handed, we first find the chance both are left-handed (using the independent events concept) and then apply the complement rule:\[ P(\text{At Least One Right-Handed}) = 1 - P(\text{Both Left-Handed}) = 1 - 0.0169 = 0.9831 \] Thus, there's a very high probability (98.31%) that at least one of the two people is right-handed. Understanding these complement relationships simplifies complex probability questions.

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

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?

In airline applications, failure of a component can result in catastrophe. As a result, many airline components utilize something called triple modular redundancy. This means that a critical component has two backup components that may be utilized should the initial component fail. Suppose a certain critical airline component has a probability of failure of 0.006 and the system that utilizes the component is part of a triple modular redundancy. (a) Assuming each component's failure/success is independent of the others, what is the probability all three components fail, resulting in disaster for the flight? (b) What is the probability at least one of the components does not fail?

A bag of 30 tulip bulbs purchased from a nursery contains 12 red tulip bulbs, 10 yellow tulip bulbs, and 8 purple tulip bulbs. Use a tree diagram like the one in Example 5 to answer the following: (a) What is the probability that two randomly selected tulip bulbs are both red? (b) What is the probability that the first bulb selected is red and the second yellow? (c) What is the probability that the first bulb selected is yellow and the second is red? (d) What is the probability that one bulb is red and the other yellow?

According to Nate Silver, the probability of a senate candidate winning his/her election with a \(5 \%\) lead in an average of polls with a week until the election is \(0.89 .\) Interpret this probability.

True or False: In a probability model, the sum of the probabilities of all outcomes must equal 1 .
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Decision Maths

Read Explanation

Statistics

Read Explanation

Calculus

Read Explanation

Mechanics Maths

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.