Probability of Selecting a Number Divisible by 5 from 1 to 20

In the world of probability and statistics, one fundamental concept is the probability of a particular event occurring. This article focuses on calculating the probability of selecting a number divisible by 5 from the range of 1 to 20. We will break down the problem into simple, understandable steps and provide a detailed explanation.

Understanding the Probability of Divisibility

Divisibility is a key concept in arithmetic where a number evenly divides another without leaving a remainder. In this context, we are interested in the probability of selecting a number from the set {1, 2, 3, ..., 20} that is divisible by 5. To solve this problem, we first need to identify the total number of outcomes and then the favorable outcomes.

Total Number of Outcomes

Let's start by determining the total number of possible outcomes. The numbers from 1 to 20 form the sample space. In this case, the sample space S is defined as:

S {1, 2, 3, ..., 19, 20}

The total number of outcomes in this sample space is 20, represented as:

n(S) 20

Favorable Outcomes

Next, we need to identify the numbers within the range that are divisible by 5. These numbers are:

5 10 15 20

Each of these numbers is divisible by 5, and there are exactly 4 numbers in this range that meet the criterion. Thus, the set of favorable outcomes is:

A {5, 10, 15, 20}

And the number of favorable outcomes is 4, denoted as:

n(A) 4

Calculating the Probability

The probability of an event is defined as the ratio of the number of favorable outcomes to the total number of outcomes. In this case, the probability (P) of selecting a number divisible by 5 is given by:

P frac{n(A)}{n(S)} frac{4}{20} frac{1}{5}

Expressed as a decimal, this probability is 0.2.

Conclusion

In summary, the probability of selecting a number from 1 to 20 that is divisible by 5 is (frac{1}{5}) or 0.2. This result is derived by identifying the total number of outcomes and the number of favorable outcomes, then applying the formula for probability.

Further Reading and Practice

To deepen your understanding of probability and divisibility, consider exploring related concepts such as:

Basic Probability Principles Divisibility Rules Combinatorial Probability

PRACTICE PROBLEMS:

Calculate the probability of selecting a number divisible by 4 from the range 1 to 25. Find the probability of selecting a number from 1 to 30 that is divisible by 6. What is the probability of selecting a number from 1 to 50 that is divisible by 7?

We encourage you to practice these problems and apply the concepts discussed in this article to a wider range of scenarios. By doing so, you will enhance your understanding of probability and its applications in various fields.

Remember, practice makes perfect, and understanding these fundamental concepts will serve as a strong foundation for more complex statistical and mathematical analyses.