To complete the table with the given information, we need to calculate the values for [tex]\(A\)[/tex] and [tex]\(B\)[/tex] based on the observed frequencies and the total number of trials.
Step-by-Step Solution:
1. Identify the total number of trials:
- We have a number cube that is rolled 60 times.
- Therefore, the total number of trials is [tex]\( 60 \)[/tex].
2. Identify the observed frequencies for which we need to find the relative frequencies:
- We have two unknown relative frequencies: [tex]\(A\)[/tex] and [tex]\(B\)[/tex].
- The observed frequencies corresponding to [tex]\(A\)[/tex] and [tex]\(B\)[/tex] are [tex]\(12\)[/tex] and [tex]\(8\)[/tex] respectively.
3. Calculate the relative frequency for each observed frequency:
- Relative frequency is calculated by dividing the observed frequency by the total number of trials.
- For [tex]\(A\)[/tex]:
[tex]\[
A = \frac{\text{observed frequency}}{\text{total trials}} = \frac{12}{60}
\][/tex]
Simplifying this fraction:
[tex]\[
A = 0.2
\][/tex]
- For [tex]\(B\)[/tex]:
[tex]\[
B = \frac{\text{observed frequency}}{\text{total trials}} = \frac{8}{60}
\][/tex]
Simplifying this fraction:
[tex]\[
B = \frac{8}{60} = \frac{8 \div 4}{60 \div 4} = \frac{2}{15} \approx 0.1333
\][/tex]
So, the relative frequencies are:
- [tex]\(A = 0.2\)[/tex]
- [tex]\(B = 0.1333\)[/tex]
Therefore, the completed table is:
\begin{tabular}{|c|c|c|}
\hline er & \begin{tabular}{c}
Observed \\
Frequency
\end{tabular} & \begin{tabular}{c}
Relative \\
Frequency
\end{tabular} \\
\hline 10 & [tex]$1 / 6$[/tex] \\
\hline 12 & [tex]$0.2$[/tex] \\
\hline 10 & [tex]$1 / 6$[/tex] \\
\hline 10 & [tex]$1 / 6$[/tex] \\
\hline 8 & [tex]$0.1333$[/tex] \\
\hline 10 & [tex]$1 / 6$[/tex] \\
\hline
\end{tabular}
This completes the table with the calculated relative frequencies for [tex]\(A\)[/tex] and [tex]\(B\)[/tex].
