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Select the correct answer.

Robin randomly selects a number between 1 and 20. What is the probability that the number selected is the square of a natural number?

A. [tex]$\frac{1}{2}$[/tex]
B. [tex]$\frac{3}{20}$[/tex]
C. [tex]$\frac{3}{10}$[/tex]
D. [tex]$\frac{1}{5}$[/tex]
E. [tex]$\frac{1}{3}$[/tex]


Sagot :

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].