To determine the relative frequency of landing on red, follow these steps:
1. Identify the Frequency of Each Color:
From the given table, we have:
- Yellow: 15 times
- Purple: 20 times
- Blue: 25 times
- Red: 25 times
- Black: 15 times
2. Find the Total Number of Trials:
Declan selected a counter 100 times in total. This means our total number of trials is:
[tex]\[
\text{Total Trials} = 100
\][/tex]
3. Determine the Frequency of Red Counters:
The frequency of landing on red is given directly from the table as:
[tex]\[
\text{Frequency of Red} = 25
\][/tex]
4. Calculate the Relative Frequency:
The relative frequency is calculated by dividing the frequency of the red counters by the total number of trials. Therefore:
[tex]\[
\text{Relative Frequency of Red} = \frac{\text{Frequency of Red}}{\text{Total Trials}}
\][/tex]
Substituting the values in, we get:
[tex]\[
\text{Relative Frequency of Red} = \frac{25}{100}
\][/tex]
5. Simplify the Fraction:
Simplifying [tex]\(\frac{25}{100}\)[/tex] results in:
[tex]\[
\frac{25}{100} = 0.25
\][/tex]
Therefore, the relative frequency of landing on a red counter is [tex]\(0.25\)[/tex].
