\begin{tabular}{|c|c|c|}
\begin{tabular}{c}
Number \\
Rolled
\end{tabular} & \begin{tabular}{c}
Observed \\
Frequency
\end{tabular} & \begin{tabular}{c}
Relative \\
Frequency
\end{tabular} \\
\hline 1 & 10 & [tex]$1 / 6$[/tex] \\
\hline 2 & 12 & [tex]$A$[/tex] \\
\hline 3 & 10 & [tex]$1 / 6$[/tex] \\
\hline 4 & 10 & [tex]$1 / 6$[/tex] \\
\hline 5 & 8 & [tex]$B$[/tex] \\
\hline 6 & 10 & [tex]$1 / 6$[/tex] \\
\hline
\end{tabular}

A number cube is rolled 60 times. The results of those 60 trials are recorded in the table. Complete the table.

[tex]$ \begin{array}{l}
A = \frac{2}{15} \\
B = \square
\end{array} $[/tex]

Options:

A. [tex]$\frac{1}{4}$[/tex]

B. [tex]$\frac{1}{5}$[/tex]

C. [tex]$\frac{1}{6}$[/tex]

D. [tex]$\frac{2}{15}$[/tex]



Answer :

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
}