/*! 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 Rolling a Die. What is the proba... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 11: Problem 7

Rolling a Die. What is the probability of rolling a number less than 4 on a die?

Short Answer

Expert verified
The probability is 0.5.

Step by step solution

01

Understand the Problem

A standard die has 6 faces, numbered from 1 to 6. The task is to find the probability of rolling a number less than 4.
02

Identify Possible Outcomes

List all possible outcomes when rolling a die: 1, 2, 3, 4, 5, and 6. Therefore, there are 6 possible outcomes.
03

Identify Favorable Outcomes

Identify the outcomes less than 4. These are: 1, 2, and 3. Therefore, there are 3 favorable outcomes.
04

Calculate the Probability

Use the probability formula: \[ P(\text{event}) = \frac{\text{number of favorable outcomes}}{\text{total number of possible outcomes}} \]Substitute the values: \[ P(\text{number less than 4}) = \frac{3}{6} = \frac{1}{2} = 0.5 \]

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.

Rolling a Die
A die is a small cube with numbers from 1 to 6 on its faces. When you roll it, it lands on one of these numbers randomly. Each roll is independent, meaning previous rolls do not affect future rolls. Rolling a die is a common way to teach probability because each face has an equal chance of landing up.
Probability Calculation
To calculate the probability of an event, we use the formula: \[ P(\text{event}) = \frac{\text{number of favorable outcomes}}{\text{total number of possible outcomes}} \] Probability tells us how likely an event is to happen. It is always a number between 0 and 1. If the probability is 0, the event cannot happen. If it is 1, the event is certain to happen. In our dice example, if we need the probability of rolling a number less than 4, we first find the favorable and possible outcomes. Then, we simply divide the number of favorable outcomes by the total possible outcomes.
Favorable Outcomes
Favorable outcomes are the specific outcomes we are interested in. For example, if we want to know the probability of rolling a number less than 4, we are only interested in the outcomes 1, 2, and 3. Hence, there are 3 favorable outcomes. Understanding favorable outcomes is key to solving any probability problem, as it narrows down the number of potential successes.
Possible Outcomes
Possible outcomes are all the outcomes that can occur. When you roll a standard die, you can get any of the numbers: 1, 2, 3, 4, 5, or 6. Therefore, there are 6 possible outcomes. Knowing the total number of possible outcomes helps in calculating the probability of any specific event, as it forms the denominator of your probability fraction. In summary, always start by listing all the possible outcomes to understand the scope of your probability problem.

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

Insert three arithmetic means between \(-3\) and 5 .

The Tower of Hanoi Problem. There are three pegs on a board. On one peg are \(n\) disks, each smaller than the one on which it rests. The problem is to move this pile of disks to another peg. The final order must be the same, but you can move only one disk at a time and can never place a larger disk on a smaller one. (IMAGE CANNOT COPY) a) What is the least number of moves needed to move 3 disks? 4 disks? 2 disks? 1 disk? b) Conjecture a formula for the least number of moves needed to move \(n\) disks. Prove it by mathematical induction.

Give your answer using permutation notation, factorial notation, or other operations. Then evaluate. How many permutations are there of the letters in each of the following words, if all the letters are used without repetition? Social Security Numbers. \(\quad\) A social security number is a 9 -digit number like \(243-47-0825\) a) How many different social security numbers can there be? b) There are about 310 million people in the United States. Can each person have a unique social security number?

For each pair of functions, find \((f \circ g)(x)\) and \((g \circ f)(x)\). $$f(x)=x^{2}, g(x)=4 x+5$$

Find the sum. \(_{n} C_{0}+_{n} C_{1}+\cdots+_{n} C_{n}\)
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Decision Maths

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

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.