/*! 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 58 Explain how to find the probabil... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 8: Problem 58

Explain how to find the probability of an event not occurring. Give an example.

Short Answer

Expert verified
To find the probability of an event not occurring, first find the probability of the event occurring and then subtract this from 1. For instance, if the probability of getting a '4' in a dice throw is \( \frac{1}{6} \), the probability of not getting a '4' is \( 1 - \frac{1}{6} = \frac{5}{6} \).

Step by step solution

01

Understand Probability

Probability is the measure of the likelihood that an event will occur. It is quantified as a number between 0 and 1. A Probability of 1 indicates certainty the event will occur, and 0 indicates the event will not occur. Probability can be calculated by dividing the number of favorable outcomes by the total number of outcomes.
02

Define the Event

An event is any outcome or combination of outcomes. For this example, consider a simple event of tossing a fair six-sided dice. The event can be getting a '4'. There are 6 possible outcomes (1, 2, 3, 4, 5, 6) and only one favorable outcome which is '4'.
03

Calculate Probability of Event Occurring

To calculate the probability of '4' occurring, divide the number of favorable outcomes (1, since '4' is just one number) by the total number of outcomes (6, since there are six faces on the dice). The probability is \( \frac{1}{6} \).
04

Calculate Probability of Event Not Occurring

The understanding that the sum of probabilities of all possible exhaustive outcomes is 1, which is the Principle of Complementarity. To get the probability of the event not occurring (not getting a '4') is calculated as 1 minus the probability of the event (getting a 4). Therefore, the probability of not getting a '4' is \( 1 - \frac{1}{6} = \frac{5}{6} \).

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!

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

Exercises \(85-87\) will help you prepare for the material covered in the next section. Use the formula \(a_{n}-a_{1} 3^{n-1}\) to find the seventh term of the sequence \(11,33,99,297, \dots\)

Write a word problem that can be solved by evaluating \(_7 P_{3}\)

Use the formula for \(_{n} C_{r}\) to solve To win in the New York State lottery, one must correctly select 6 numbers from 59 numbers. The order in which the selection is made does not matter. How many different selections are possible?

Solve by the method of your choice. Fifty people purchase raffle tickets. Three winning tickets are selected at random. If first prize is \(\$ 1000,\) second prize is \(\$ 500\) and third prize is \(\$ 100,\) in how many different ways can the prizes be awarded?

Use the formula for \(_{n} P_{r}\) to solve Exercises \(41-48\) How many arrangements can be made using four of the letters of the word COMBINE if no letter is to be used more than once?
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Discrete Mathematics

Read Explanation

Applied Mathematics

Read Explanation

Geometry

Read Explanation

Pure Maths

Read Explanation

Logic and Functions

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.