/*! 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 20 Express the indicated degree of ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 20

Express the indicated degree of likelihood as a probability value between 0 and \(1 .\) Benjamin Franklin said that death is a certainty of life.

Short Answer

Expert verified
The probability value is 1.

Step by step solution

01

Understand the Concept of Probability

Probability value ranges between 0 and 1. A probability of 0 means the event will not happen, while a probability of 1 means the event is certain to happen.
02

Identify the Degree of Likelihood

Benjamin Franklin stated that death is a certainty of life. This means that the likelihood of death occurring is 100%.
03

Convert Likelihood to Probability

Since the likelihood of death is 100%, we can express this as a probability value. A 100% likelihood is equal to a probability value of 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!

Key Concepts

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

probability value
Probability is a way to measure how likely an event is to happen. It's a value that ranges from 0 to 1.
The value 0 means the event will definitely not happen, and the value 1 means the event will definitely happen.

Think about flipping a fair coin. The probability of getting heads is 0.5, because it can land on either heads or tails, giving it a 50% chance or 0.5 as a probability.
To sum it up:
  • 0 means impossible
  • 1 means certain
  • Values in between show the degree of possibility
This scale helps us understand and predict events.
certainty
Certainty in probability refers to an event that will unquestionably occur. When we say something is certain, the probability is 1.

Imagine the sun rising tomorrow. We consider it certain because it happens every day. The probability of the sun rising tomorrow is therefore 1.

In the exercise example, Benjamin Franklin stated that death is a certainty in life. This means that, no matter what, death will happen.
Thus, the probability value for this event is 1.
likelihood
Likelihood is a term often used interchangeably with probability, but they can have nuanced differences. Likelihood refers to how probable we believe an event is based on given information.

For instance, if weather forecasts predict rain, the likelihood of carrying an umbrella increases. The forecast gives us information that rain is probable.

Using our example again, since death is presented as a certainty by Benjamin Franklin, the likelihood of death happening is 100%.
This makes the event's probability value 1, confirming it is certain.

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

Let \(A=\) the event of getting at least 1 defective iPhone when 3 iPhones are randomly selected with replacement from a batch. If \(5 \%\) of the iPhones in a batch are defective and the other \(95 \%\) are all good, which of the following are correct? a. \(P(\bar{A})=(0.95)(0.95)(0.95)=0.857\) b. \(P(A)=1-(0.95)(0.95)(0.95)=0.143\) c. \(P(A)=(0.05)(0.05)(0.05)=0.000125\)

Find the indicated complements. When the author observed a sobriety checkpoint conducted by the Dutchess County Sheriff Department, he saw that 676 drivers were screened and 6 were arrested for driving while intoxicated. Based on those results, we can estimate that \(P(I)=0.00888\), where \(I\) denotes the event of screening a driver and getting someone who is intoxicated. What does \(P(\bar{I})\) denote, and what is its value?

While this exercise was being created, Weather.com indicated that there was a \(60 \%\) chance of rain for the author's home region. Based on that report, which of the following is the most reasonable interpretation? a. \(60 \%\) of the author's region will get rain today. b. In the author's region, it will rain for \(60 \%\) of the day. c. There is a \(0.60\) probability that it will rain somewhere in the author's region at some point during the day.

Express all probabilities as fractions. Clinical trials of Nasonex involved a group given placebos and another group given treatments of Nasonex. Assume that a preliminary phase I trial is to be conducted with 12 subjects, including 6 men and 6 women. If 6 of the 12 subjects are randomly selected for the treatment group, find the probability of getting 6 subjects of the same gender. Would there be a problem with having members of the treatment group all of the same gender?

Express all probabilities as fractions. A presidential candidate plans to begin her campaign by visiting the capitals of 5 of the 50 states. If the five capitals are randomly selected without replacement, what is the probability that the route is Sacramento, Albany, Juneau, Hartford, and Bismarck, in that order?
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Decision Maths

Read Explanation

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Geometry

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.