A Six-sided Number Cube Is Rolled Twice. What Is The Probability That The First Roll Is An Even Number And The Second Roll Is A Number Greater Than 4?A. { \frac{1}{6}$}$ B. { \frac{1}{3}$}$ C. { \frac{2}{3}$}$ D.
Introduction
Probability is a fundamental concept in mathematics that deals with the likelihood of an event occurring. In this article, we will explore the concept of probability using a simple example involving a six-sided number cube. We will calculate the probability of rolling an even number on the first roll and a number greater than 4 on the second roll.
What is a Six-Sided Number Cube?
A six-sided number cube, also known as a die, is a cube-shaped object with six faces, each marked with a different number from 1 to 6. When a die is rolled, the number on the face that lands facing up is the result.
The Problem: Rolling an Even Number and a Number Greater than 4
We are asked to find the probability that the first roll is an even number and the second roll is a number greater than 4.
Step 1: Determine the Probability of Rolling an Even Number on the First Roll
To roll an even number on the first roll, we need to consider the possible outcomes. There are three even numbers on a six-sided die: 2, 4, and 6. The probability of rolling an even number on the first roll is therefore:
3/6 = 1/2
This means that there is a 50% chance of rolling an even number on the first roll.
Step 2: Determine the Probability of Rolling a Number Greater than 4 on the Second Roll
To roll a number greater than 4 on the second roll, we need to consider the possible outcomes. There are two numbers greater than 4 on a six-sided die: 5 and 6. The probability of rolling a number greater than 4 on the second roll is therefore:
2/6 = 1/3
This means that there is a 33.33% chance of rolling a number greater than 4 on the second roll.
Step 3: Calculate the Probability of Both Events Occurring
Since the two events are independent (the outcome of the first roll does not affect the outcome of the second roll), we can multiply the probabilities of each event to find the probability of both events occurring:
(1/2) × (1/3) = 1/6
This means that there is a 16.67% chance of rolling an even number on the first roll and a number greater than 4 on the second roll.
Conclusion
In this article, we used a simple example involving a six-sided number cube to illustrate the concept of probability. We calculated the probability of rolling an even number on the first roll and a number greater than 4 on the second roll, and found that the probability of both events occurring is 1/6.
Answer
The correct answer is A. .
Additional Examples and Exercises
- What is the probability of rolling a number less than 3 on a six-sided die?
- What is the probability of rolling an odd number on a six-sided die?
- What is the probability of rolling a number greater than 2 on a six-sided die?
These exercises will help you practice calculating probabilities using a six-sided number cube.
References
Glossary
- Probability: A measure of the likelihood of an event occurring.
- Independent events: Events that do not affect each other.
- Six-sided die: A cube-shaped object with six faces, each marked with a different number from 1 to 6.
A Six-Sided Number Cube: Frequently Asked Questions =====================================================
Introduction
In our previous article, we explored the concept of probability using a simple example involving a six-sided number cube. In this article, we will answer some frequently asked questions related to six-sided number cubes and probability.
Q: What is the probability of rolling a number less than 3 on a six-sided die?
A: To roll a number less than 3 on a six-sided die, we need to consider the possible outcomes. There are two numbers less than 3 on a six-sided die: 1 and 2. The probability of rolling a number less than 3 on a six-sided die is therefore:
2/6 = 1/3
This means that there is a 33.33% chance of rolling a number less than 3 on a six-sided die.
Q: What is the probability of rolling an odd number on a six-sided die?
A: To roll an odd number on a six-sided die, we need to consider the possible outcomes. There are three odd numbers on a six-sided die: 1, 3, and 5. The probability of rolling an odd number on a six-sided die is therefore:
3/6 = 1/2
This means that there is a 50% chance of rolling an odd number on a six-sided die.
Q: What is the probability of rolling a number greater than 2 on a six-sided die?
A: To roll a number greater than 2 on a six-sided die, we need to consider the possible outcomes. There are four numbers greater than 2 on a six-sided die: 3, 4, 5, and 6. The probability of rolling a number greater than 2 on a six-sided die is therefore:
4/6 = 2/3
This means that there is a 66.67% chance of rolling a number greater than 2 on a six-sided die.
Q: What is the probability of rolling a number less than 4 on a six-sided die?
A: To roll a number less than 4 on a six-sided die, we need to consider the possible outcomes. There are three numbers less than 4 on a six-sided die: 1, 2, and 3. The probability of rolling a number less than 4 on a six-sided die is therefore:
3/6 = 1/2
This means that there is a 50% chance of rolling a number less than 4 on a six-sided die.
Q: What is the probability of rolling a number greater than 5 on a six-sided die?
A: To roll a number greater than 5 on a six-sided die, we need to consider the possible outcomes. There is one number greater than 5 on a six-sided die: 6. The probability of rolling a number greater than 5 on a six-sided die is therefore:
1/6
This means that there is a 16.67% chance of rolling a number greater than 5 on a six-sided die.
Q: What is the probability of rolling a number less than 6 on a six-sided die?
A: To roll a number less than 6 on a six-sided die, we need to consider the possible outcomes. There are five numbers less than 6 on a six-sided die: 1, 2, 3, 4, and 5. The probability of rolling a number less than 6 on a six-sided die is therefore:
5/6
This means that there is a 83.33% chance of rolling a number less than 6 on a six-sided die.
Conclusion
In this article, we answered some frequently asked questions related to six-sided number cubes and probability. We calculated the probability of rolling various numbers on a six-sided die, including numbers less than 3, odd numbers, numbers greater than 2, numbers less than 4, numbers greater than 5, and numbers less than 6.
Answer Key
- Q1: 1/3
- Q2: 1/2
- Q3: 2/3
- Q4: 1/2
- Q5: 1/6
- Q6: 5/6
Additional Examples and Exercises
- What is the probability of rolling a number between 2 and 5 on a six-sided die?
- What is the probability of rolling an even number on a six-sided die?
- What is the probability of rolling a number greater than 1 on a six-sided die?
These exercises will help you practice calculating probabilities using a six-sided number cube.
References
Glossary
- Probability: A measure of the likelihood of an event occurring.
- Independent events: Events that do not affect each other.
- Six-sided die: A cube-shaped object with six faces, each marked with a different number from 1 to 6.