To determine the relative frequency of each letter picked by Joshua, Audrey, and Simone, we first need to understand the concept of relative frequency. Relative frequency is the fraction or proportion of the total number of trials that a particular outcome occurs. It can be calculated using the formula:
[tex]\[ \text{Relative Frequency} = \frac{\text{Number of Times the Event Occurs}}{\text{Total Number of Trials}} \][/tex]
Given the total number of picks (trials) is 120, we can now calculate the relative frequency for each letter.
1. Relative frequency of picking [tex]\(A\)[/tex]:
- Number of times [tex]\(A\)[/tex] was picked: 24
- Total number of picks: 120
[tex]\[
\text{Relative Frequency of } A = \frac{24}{120} = 0.2
\][/tex]
2. Relative frequency of picking [tex]\(B\)[/tex]:
- Number of times [tex]\(B\)[/tex] was picked: 66
- Total number of picks: 120
[tex]\[
\text{Relative Frequency of } B = \frac{66}{120} = 0.55
\][/tex]
3. Relative frequency of picking [tex]\(C\)[/tex]:
- Number of times [tex]\(C\)[/tex] was picked: 30
- Total number of picks: 120
[tex]\[
\text{Relative Frequency of } C = \frac{30}{120} = 0.25
\][/tex]
Thus, the relative frequencies are:
- The relative frequency of picking [tex]\(A\)[/tex] is [tex]\(0.2\)[/tex].
- The relative frequency of picking [tex]\(B\)[/tex] is [tex]\(0.55\)[/tex].
- The relative frequency of picking [tex]\(C\)[/tex] is [tex]\(0.25\)[/tex].
