Certainly! Let's break down the problem step-by-step.
1. Understanding the Problem:
- We need to find the probability that a randomly selected number between 1 and 20 is a square of a natural number.
2. Range of Numbers:
- The range of numbers Robin can select from is 1 to 20, inclusive. This means Robin can pick any number from 1 to 20.
3. Identify the Squares of Natural Numbers within the Range:
- A natural number is a positive integer (1, 2, 3, ...).
- We need to find the squares of these natural numbers that lie between 1 and 20.
- The squares of natural numbers are:
- [tex]\(1^2 = 1\)[/tex]
- [tex]\(2^2 = 4\)[/tex]
- [tex]\(3^2 = 9\)[/tex]
- [tex]\(4^2 = 16\)[/tex]
- These squares are [tex]\(1, 4, 9,\)[/tex] and [tex]\(16\)[/tex].
4. Count the Squares:
- There are 4 numbers (1, 4, 9, 16) that are squares of natural numbers and fall within the range of 1 to 20.
5. Calculate the Total Number of Possible Outcomes:
- There are 20 possible numbers that Robin can pick (1 through 20).
6. Determine the Probability:
- Probability is calculated as the ratio of favorable outcomes to the total number of possible outcomes.
- Here, the favorable outcomes are the numbers that are squares of natural numbers (4 numbers), and the total outcomes are 20.
[tex]\[
\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{4}{20} = \frac{1}{5}
\][/tex]
7. Conclusion:
- The probability that the number selected is the square of a natural number is [tex]\(\frac{1}{5}\)[/tex].
Therefore, the correct answer is D. [tex]\(\frac{1}{5}\)[/tex].
