/*! 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 3 One die is rolled. What is the p... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 3

One die is rolled. What is the probability of not getting a \(5 ?\)

Short Answer

Expert verified
The probability of not getting a 5 when a die is rolled is \(\frac{5}{6}\).

Step by step solution

01

Determine Total Outcomes

There are 6 possible outcomes when rolling a standard die, as it has 6 faces, each with a different number ranging from 1 to 6 inclusive.
02

Determine Favorable Outcomes

Since we're looking for the likelihood of not getting a 5, we're interested in any outcome that does not result in a 5. With this, there 5 favorable outcomes: rolling a 1, 2, 3, 4 or 6.
03

Calculate the Probability

In probability, we calculate the likelihood of an event happening by dividing the number of favorable outcomes by the total outcomes. Therefore, here the probability is \(\frac{5}{6}\).

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!

Key Concepts

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

Total Outcomes
When you're rolling a die, understanding the concept of total outcomes is crucial. A standard six-sided die, which is commonly used in games and probability exercises, has 6 distinct faces. Each face represents a different number from 1 to 6. So, every time you roll the die, there are exactly 6 possible outcomes you could get.

These outcomes can be listed as follows:
  • Outcome 1: Rolled a 1
  • Outcome 2: Rolled a 2
  • Outcome 3: Rolled a 3
  • Outcome 4: Rolled a 4
  • Outcome 5: Rolled a 5
  • Outcome 6: Rolled a 6
Total outcomes refer to all the potential results from a single event.
By clearly understanding this, you can better assess which results are relevant to any given question about probability.
Favorable Outcomes
The idea of favorable outcomes focuses on the specific outcomes that meet the criteria of the event you're examining. In probability problems, it's common to focus on specific desired results.

For instance, when asked about the probability of NOT rolling a 5 on a single roll of a die, we consider which outcomes do not include the number 5. In this scenario, the favorable outcomes are:
  • Rolling a 1
  • Rolling a 2
  • Rolling a 3
  • Rolling a 4
  • Rolling a 6
There are 5 favorable outcomes because each one represents a roll that does not produce a 5.
The favorable outcomes determine which numbers will contribute to calculating the desired probability.
Rolling a Die
Rolling a die is a simple but important concept in probability. It serves as a classic exercise to explore probability fundamentals. Each roll of a die is an independent event, meaning previous rolls do not affect future rolls.

This randomness makes dice excellent tools for teaching how to calculate probabilities, as the outcomes are easy to predict and enumerated clearly. Understanding rolling a die involves knowing:
  • Each face has an equal chance of landing face up.
  • For a fair die, each face has a probability of 1 out of 6, or roughly 16.67%.
It's important to consider the role of randomness and equality when using a die in probability.
This planning helps introduce greater concepts in probability and paves the way for tackling more complex scenarios.

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

If the coin is flipped 10 times, what is the probability of at least one head given at least one tail?

Prove that \(2 C(2 n-1, n)=C(2 n, n)\) for all \(n \geq 1\).

What is wrong with the following argument, which supposedly counts the number of partitions of a 10 -element set into eight (nonempty) subsets? List the elements of the set with blanks between them: $$x_{1}-x_{2}-x_{3}-x_{4}-x_{5}-x_{6}-x_{7}-x_{8}-x_{9}-x_{10}$$ Every time we fill seven of the nine blanks with seven vertical bars, we obtain a partition of \(\left\\{x_{1}, \ldots, x_{10}\right\\}\) into eight subsets. For example, the partition \(\left\\{x_{1}\right\\},\left\\{x_{2}\right\\},\left\\{x_{3}, x_{4}\right\\}\left\\{x_{5}\right\\},\left\\{x_{6}\right\\},\) \(\left\\{x_{7}, x_{8}\right\\}\left\\{x_{9}\right\\},\left\\{x_{10}\right\\}\) would be represented as $$x_{1}\left|x_{2}\right| x_{3} x_{4}\left|x_{5}\right| x_{6}\left|x_{7} x_{8}\right| x_{9} \mid x_{10}$$ Thus the solution to the problem is \(C(9,7)\).

Prove that a planar polygon with \(n\) sides, \(n \geq 3,\) has at least three interior angles each less than 180 degrees. Assume no 0-degree interior angles. As an example, in the following figure angles \(A, C,\) and \(E\) are each less than 180 degrees.

Exercises \(47-50\) ask about the following situation. In a small charity fundraiser, 70 tickets are sold numbered 1 through \(70 .\) Each person buys one ticket. Later in the evening. 20 numbers are randomly drawn from among \(I\) through 70 , and those holding these numbers win modest prizes. Among those buying the tickets are Maya and Chloe. What is the probability that both Maya and Chloe win prizes?
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Probability and Statistics

Read Explanation

Pure Maths

Read Explanation

Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Applied Mathematics

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.