Problem 12 If a die is rolled, in how many ... [FREE SOLUTION]

91影视

Prealgebra

Julie Miller, Molly O鈥橬eill, Nancy Hyde

$Math Studyset 91影视 Explanations$ Math

1 Edition

Chapter 9: Problem 12

If a die is rolled, in how many ways can a number less than 6 come up?

Short Answer

Expert verified

There are 5 ways.

Step by step solution

Identify the Problem

Determine how many possible outcomes on a die are less than 6.

Review Possible Outcomes of a Die Roll

A standard die has the following faces: 1, 2, 3, 4, 5, and 6.

Identify Outcomes Less Than 6

The numbers less than 6 on a die are: 1, 2, 3, 4, and 5.

Count the Valid Outcomes

Count the number of valid outcomes identified in the previous step. There are 5 outcomes: 1, 2, 3, 4, and 5.

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.

Die Roll Outcomes

When rolling a standard six-sided die, each of the sides鈥攏umbered from 1 to 6鈥攃an land face up. These side numbers are the possible outcomes of a die roll.

Understanding the outcomes is crucial in identifying the likelihood of various results. Knowledge of these numbers forms the foundation of probability calculations.

A die has 6 faces
Possible outcomes are: 1, 2, 3, 4, 5, and 6

Every roll can result in any one of these numbers with equal likelihood, making each outcome fair and unbiased. Additionally, the total number of outcomes directly impacts more complex probability calculations.

Counting Outcomes

Counting the number of possible outcomes is an essential part of probability problems. It's important to consider all potential results when evaluating the scenarios described. If you want to know how many ways a number less than 6 can appear, you need to count every relevant outcome.

In our exercise:

Outcomes of a die roll are 1, 2, 3, 4, 5, and 6
Numbers less than 6 are: 1, 2, 3, 4, and 5

By counting these, you see there are five outcomes less than 6.

Thus, for a die rolled once, there are 5 ways a number less than 6 can appear. Understanding this counting method ensures accuracy in solving probability problems.

Valid Outcomes

When solving probability problems, identifying valid outcomes is vital. Valid outcomes are those that meet the problem's specific criteria. In our scenario, we need numbers less than 6 in a die roll. Defining these outcomes correctly ensures accurate calculations.

From the exercise, we see:

Possible numbers on a die are 1, 2, 3, 4, 5, and 6
Valid outcomes (less than 6): 1, 2, 3, 4, and 5

By specifying the valid outcomes, you can tackle the probability problem confidently. This step makes the rest of the probability calculation clear and straightforward, providing a stepping stone for more complex questions in the future.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

If a die is rolled, in how many ways can a number less than 6 come up?

Short Answer

Step by step solution

Identify the Problem

Review Possible Outcomes of a Die Roll

Identify Outcomes Less Than 6

Count the Valid Outcomes

Key Concepts

Die Roll Outcomes

Counting Outcomes

Valid Outcomes

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Pure Maths

Theoretical and Mathematical Physics

Probability and Statistics

Decision Maths

Logic and Functions

Study anywhere. Anytime. Across all devices.