Understanding Multiples of 4

Oct 13, 2025 by miodeya.com 68 views

Introduction

In probability theory, the probability of an event is a measure of the likelihood that the event will occur. In this article, we will explore the probability of selecting a multiple of 4 from the numbers 1 to 15. This problem is a classic example of a discrete probability distribution, where we have a finite number of outcomes and each outcome has a certain probability of occurring.

Understanding Multiples of 4

To begin with, let's understand what multiples of 4 are. A multiple of 4 is a number that can be divided by 4 without leaving a remainder. For example, 4, 8, 12, and 16 are all multiples of 4. In the context of this problem, we are interested in finding the probability of selecting a multiple of 4 from the numbers 1 to 15.

Counting the Multiples of 4

To calculate the probability of selecting a multiple of 4, we need to count the number of multiples of 4 in the range 1 to 15. We can do this by listing out the multiples of 4 in this range: 4, 8, 12, and 16. However, we need to be careful not to include numbers that are greater than 15. Therefore, we will only consider the multiples of 4 that are less than or equal to 15.

Calculating the Probability

Now that we have counted the number of multiples of 4 in the range 1 to 15, we can calculate the probability of selecting a multiple of 4. The probability of an event is defined as the number of favorable outcomes divided by the total number of possible outcomes. In this case, the number of favorable outcomes is the number of multiples of 4 in the range 1 to 15, which is 4. The total number of possible outcomes is the total number of numbers in the range 1 to 15, which is 15.

Applying the Formula

To calculate the probability, we can apply the formula:

Probability = Number of favorable outcomes / Total number of possible outcomes

In this case, the probability is:

Probability = 4 / 15

Simplifying the Fraction

The fraction 4/15 cannot be simplified further, so this is the final answer.

Conclusion

In conclusion, the probability of selecting a multiple of 4 from the numbers 1 to 15 is 4/15. This problem is a classic example of a discrete probability distribution, where we have a finite number of outcomes and each outcome has a certain probability of occurring. By counting the number of multiples of 4 in the range 1 to 15 and applying the formula for probability, we were able to calculate the probability of selecting a multiple of 4.

Final Answer

The final answer is $\boxed{\frac{4}{15}}$ .

Additional Examples

Here are a few additional examples of how to calculate the probability of selecting a multiple of a number from a range of numbers:

The probability of selecting a multiple of 3 from the numbers 1 to 20 is 6/20 = 3/10.
The probability of selecting a multiple of 5 from the numbers 1 to 25 is 5/25 = 1/5.
The probability of selecting a multiple of 2 from the numbers 1 to 18 is 9/18 = 1/2.

Tips and Tricks

Here are a few tips and tricks for calculating the probability of selecting a multiple of a number from a range of numbers:

Make sure to count the number of multiples of the number in the range correctly.
Use the formula for probability to calculate the probability.
Simplify the fraction if possible.

Common Mistakes

Here are a few common mistakes to avoid when calculating the probability of selecting a multiple of a number from a range of numbers:

Not counting the number of multiples of the number in the range correctly.
Not using the formula for probability to calculate the probability.
Not simplifying the fraction if possible.

Real-World Applications

The concept of probability is used in many real-world applications, including:

Insurance: Probability is used to calculate the likelihood of an event occurring, such as a car accident or a natural disaster.
Finance: Probability is used to calculate the likelihood of a stock or bond performing well or poorly.
Medicine: Probability is used to calculate the likelihood of a patient responding to a treatment or developing a disease.

Conclusion

Q: What is the probability of selecting a multiple of 4 from the numbers 1 to 20?

A: To calculate the probability of selecting a multiple of 4 from the numbers 1 to 20, we need to count the number of multiples of 4 in this range. The multiples of 4 in this range are 4, 8, 12, 16, and 20. Therefore, the probability of selecting a multiple of 4 is 5/20 = 1/4.

Q: What is the probability of selecting a multiple of 3 from the numbers 1 to 25?

A: To calculate the probability of selecting a multiple of 3 from the numbers 1 to 25, we need to count the number of multiples of 3 in this range. The multiples of 3 in this range are 3, 6, 9, 12, 15, 18, 21, and 24. Therefore, the probability of selecting a multiple of 3 is 8/25.

Q: What is the probability of selecting a multiple of 5 from the numbers 1 to 30?

A: To calculate the probability of selecting a multiple of 5 from the numbers 1 to 30, we need to count the number of multiples of 5 in this range. The multiples of 5 in this range are 5, 10, 15, 20, 25, and 30. Therefore, the probability of selecting a multiple of 5 is 6/30 = 1/5.

Q: What is the probability of selecting a multiple of 2 from the numbers 1 to 18?

A: To calculate the probability of selecting a multiple of 2 from the numbers 1 to 18, we need to count the number of multiples of 2 in this range. The multiples of 2 in this range are 2, 4, 6, 8, 10, 12, 14, and 16. Therefore, the probability of selecting a multiple of 2 is 8/18 = 4/9.

Q: How do I calculate the probability of selecting a multiple of a number from a range of numbers?

A: To calculate the probability of selecting a multiple of a number from a range of numbers, you need to follow these steps:

Count the number of multiples of the number in the range.
Divide the number of multiples by the total number of numbers in the range.
Simplify the fraction if possible.

Q: What is the difference between probability and odds?

A: Probability and odds are related but distinct concepts. Probability is a measure of the likelihood of an event occurring, while odds are a measure of the ratio of the probability of an event occurring to the probability of the event not occurring.

Q: How do I use probability in real-world applications?

A: Probability is used in many real-world applications, including:

Insurance: Probability is used to calculate the likelihood of an event occurring, such as a car accident or a natural disaster.
Finance: Probability is used to calculate the likelihood of a stock or bond performing well or poorly.
Medicine: Probability is used to calculate the likelihood of a patient responding to a treatment or developing a disease.

Q: What are some common mistakes to avoid when calculating probability?

A: Some common mistakes to avoid when calculating probability include:

Not counting the number of multiples of the number in the range correctly.
Not using the formula for probability to calculate the probability.
Not simplifying the fraction if possible.

Q: How do I simplify a fraction?

A: To simplify a fraction, you need to find the greatest common divisor (GCD) of the numerator and denominator and divide both numbers by the GCD.

Q: What is the greatest common divisor (GCD)?

A: The greatest common divisor (GCD) of two numbers is the largest number that divides both numbers without leaving a remainder.