To complete the table and identify the relative frequencies [tex]\( A \)[/tex] and [tex]\( B \)[/tex], given the observed frequencies and total number of rolls (60), follow these steps:
1. Calculate [tex]\( A \)[/tex]:
- The number 2 was rolled 12 times out of the total 60 rolls.
- Relative frequency [tex]\( A \)[/tex] is the ratio of the observed frequency of 2 to the total number of rolls.
Therefore, the relative frequency for 2 is:
[tex]\[
A = \frac{12}{60} = 0.2
\][/tex]
2. Calculate [tex]\( B \)[/tex]:
- The number 5 was rolled 8 times out of the total 60 rolls.
- Relative frequency [tex]\( B \)[/tex] is the ratio of the observed frequency of 5 to the total number of rolls.
Therefore, the relative frequency for 5 is:
[tex]\[
B = \frac{8}{60} \approx 0.13333333333333333
\][/tex]
By inspecting the options given for [tex]\( A \)[/tex] (assuming it's incorrectly labeled) and [tex]\( B \)[/tex]:
- For [tex]\( A \)[/tex]:
[tex]\[
A = 0.2 = \frac{2}{10} = \frac{1}{5}
\][/tex]
- For [tex]\( B \)[/tex]:
[tex]\[
B \approx 0.13333333333333333 = \frac{2}{15}
\][/tex]
So, the right matching for the frequencies are:
[tex]\[
A = 0.2 = \frac{2}{10} = \frac{1}{5}
\][/tex]
[tex]\[
B = \frac{2}{15}
\][/tex]
Hence, the entries in the table should be:
[tex]\[
A = \frac{1}{5}
\][/tex]
[tex]\[
B = \frac{2}{15}
\][/tex]
Therefore, the completed answer options should be:
\begin{align}
A &= \frac{1}{5} \\
B &= \frac{2}{15}
\end{align}
