/*! 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 2 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 2

One die is rolled. What is the probability of getting an even number?

Short Answer

Expert verified
The probability of rolling an even number on a die is \(\frac{1}{2}\) or 0.5.

Step by step solution

01

Identify the favourable outcomes

The favourable outcomes are those that satisfy the desired event. In this case, the desired event is 'getting an even number'. Since the even numbers on a standard die are 2, 4 and 6, these represent the favourable outcomes.
02

Count the total number of outcomes

The total number of outcomes when rolling a die are 6, as a standard die has six faces, each with a unique number from 1 to 6.
03

Calculate the probability

Probability is found by dividing the number of favourable outcomes by the total number of outcomes. Therefore, in this case, with 3 favourable outcomes (the even numbers) and 6 total outcomes (all the faces of the die), the probability is calculated as \(\frac{3}{6}\).

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.

Favorable Outcomes
When solving probability problems, it's crucial to understand the concept of 'favorable outcomes.' These outcomes are the desired results that match the criteria of the event we're interested in.

For instance, if you roll a standard six-sided die and want to know the probability of getting an even number, you consider the even numbers (2, 4, and 6) as the favorable outcomes because they satisfy the condition we're looking at. Identifying these outcomes correctly is the first step in any probability calculation because they represent successes in the context of the problem we're attempting to solve.
Total Number of Outcomes
The 'total number of outcomes' refers to the complete set of all possible results that can occur from a particular event.

In the context of rolling a die, there are six sides, each with a distinct number between 1 and 6. This means the total number of outcomes is 6. These outcomes form the denominator in the probability fraction because they represent the full scope of possibilities we must consider when calculating the likelihood of an event.
Probability Calculation
To calculate the probability of a specific event, the number of favorable outcomes is divided by the total number of possible outcomes. This calculation provides a value between 0 and 1, where 0 indicates impossibility and 1 indicates certainty.

In our example of rolling a die, with 3 favorable outcomes (even numbers) and 6 total outcomes, the probability is \(\frac{3}{6}\). Simplifying this fraction gives us \(\frac{1}{2}\), which means there's a 50% chance of rolling an even number on a six-sided die. The calculation reflects how likely the event is to happen in a single trial.
Discrete Mathematics
Probability is a fundamental part of discrete mathematics, which deals with countable, distinct elements. Unlike continuous mathematics, which deals with objects that can vary smoothly, discrete mathematics works with individual points.

In the case of rolling a die, each side and its corresponding number is a discrete element. The field of discrete mathematics provides the tools we use to analyze and understand such probability problems, ensuring our approach is both systematic and grounded in sound mathematical principles.

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

Prove that if \(f\) is a function from the finite set \(X\) to the finite set \(Y\) and \(|X|>|Y|,\) then \(f\) is not one-to-one.

If the coin is flipped 10 times, what is the probability of exactly five heads?

In how many ways can 15 identical computer science books and 10 identical psychology books be distributed among five students?

If \(E\) and \(F\) are independent events, are \(\bar{E}\) and \(\bar{F}\) independent?

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 \(C(9,7)\).
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

Read Explanation

Statistics

Read Explanation

Probability and Statistics

Read Explanation

Mechanics 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.