/*! 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 7 If an event cannot happen, what ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 7

If an event cannot happen, what value is assigned to its probability?

Short Answer

Expert verified
The probability assigned is 0.

Step by step solution

01

Understanding Probability

Probability is a measure of the likelihood of an event occurring, ranging from 0 to 1. A probability of 0 means the event cannot happen, while a probability of 1 means the event is certain to happen.
02

Defining Impossibility

If an event cannot happen under any circumstances, it is considered an impossible event. An impossible event has no chance of occurring.
03

Assigning Probability to Impossible Events

Since impossible events have no chance of occurring, they are assigned a probability of 0. This makes intuitive sense because 0 represents the complete lack of possibility.

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.

Impossible Event
In probability, an impossible event is an outcome that cannot occur under any circumstances. Think of it like rolling a 7 on a standard six-sided die; there's simply no way for that to happen. Impossible events are characterized by having absolutely no chance of occurring.
To further break this down:
  • Impossibility means a complete absence of any chance.
  • The event's non-occurrence is certain by definition.
  • These events help set the lower bound in probability theory.
A good way to remember this concept is by understanding that there are no situations or conditions that could lead to an impossible event occurring. When considering different scenarios, impossible events serve as a baseline to compare other, more likely events against.
Probability Value
Probability value is a numerical figure ranging from 0 to 1. It quantifies how likely an event is to happen. In this context:
  • A probability value of 0 corresponds to an impossible event, meaning there's no chance it will occur.
  • A probability value of 1 indicates a certain event, meaning it is guaranteed to happen.
  • Values between 0 and 1 indicate varying degrees of likelihood.
Expressed as a fraction, decimal, or percentage, probability values offer a standardized way to communicate the chances of events. Usually, the sum of probabilities for all possible outcomes of a situation adds up to 1. This ensures that all possibilities are accounted for and gives structure to probabilistic calculations.
Likelihood of Occurrence
The likelihood of occurrence refers to how probable an event is in a given experimental or real-world context. It's an intuitive concept applicable to everyday situations. Understanding it can help predict and plan for various outcomes.
Here are some key points:
  • Likelihood assesses the chances of an event happening.
  • It is reflected in the probability value assigned to an event.
  • The greater the likelihood, the closer the probability value is to 1.
Assessing likelihood involves considering factors that influence the event, such as conditions or past patterns. This helps in making informed predictions. A strong grasp of likelihood allows one to understand not just theoretical constructs, but practically all observable events around us.

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

Passwords Given the characters \(A, B, C, H, I, T, U, V,\) \(1,2,3,\) and \(4,\) how many seven-character passwords can be made? (No repeats are allowed.) How many if you have to use all four numbers as the first four characters in the password?

Defective Resistors A package contains 12 resistors, 3 of which are defective. If 4 are selected, find the probability of getting $$ \begin{array}{l}{\text { a. } 0 \text { defective resistors }} \\ {\text { b. } 1 \text { defective resistor }} \\ {\text { c. } 3 \text { defective resistors }}\end{array} $$

Selecting Posters A buyer decides to stock 8 different posters. How many ways can she select these 8 if there are 20 from which to choose?

Football Team Selection A football team consists of 20 freshmen and 20 sophomores, 15 juniors, and 10 seniors. Four players are selected at random to serve as captains. Find the probability that $$ \begin{array}{l}{\text { a. All } 4 \text { are seniors }} \\ {\text { b. There is } 1 \text { each: freshman, sophomore, junior, and senior }} \\\ {\text { c. There are } 2 \text { sophomores and } 2 \text { freshmen }} \\\ {\text { d. At least } 1 \text { of the students is a senior }}\end{array} $$

Buffet Desserts In how many ways can you choose 3 kinds of ice cream and 2 toppings from a dessert buffet with 10 kinds of ice cream and 6 kinds of toppings?
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Applied Mathematics

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

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.