Answered

Nathan rolls a number cube and records the result of each roll in the table.

\begin{tabular}{|c|c|}
\hline
\multicolumn{2}{|c|}{ Number Cube } \\
\hline
Number Rolled & Frequency \\
\hline
1 & 11 \\
\hline
2 & 16 \\
\hline
3 & 14 \\
\hline
4 & 20 \\
\hline
5 & 12 \\
\hline
6 & 17 \\
\hline
\end{tabular}

Which statements below represent the situation? Select three options.

A. The relative frequency of rolling a 4 is [tex]$\frac{2}{9}$[/tex].
B. The experimental probability of rolling a 3 is greater than the theoretical probability of rolling a 3.
C.



Answer :

Let's analyze the question step-by-step.

1. Calculate the total number of rolls.
Add up all the frequencies:
[tex]\[ 11 + 16 + 14 + 20 + 12 + 17 = 90 \][/tex]
So, the total number of rolls is 90.

2. Calculate the relative frequency of rolling a 4.
The frequency of rolling a 4 is 20. Therefore, the relative frequency is:
[tex]\[ \frac{20}{90} \approx 0.2222 \approx \frac{2}{9} \][/tex]
Therefore, the statement "The relative frequency of rolling a 4 is [tex]\(\frac{2}{9}\)[/tex]" is correct.

3. Calculate the experimental probability of rolling a 3.
The frequency of rolling a 3 is 14. Thus, the experimental probability is:
[tex]\[ \frac{14}{90} \approx 0.1556 \][/tex]

4. Calculate the theoretical probability of rolling any specific number on a fair cube.
A fair number cube (die) has 6 faces, and each face has an equal probability of appearing:
[tex]\[ \frac{1}{6} \approx 0.1667 \][/tex]

5. Compare the experimental probability of rolling a 3 with the theoretical probability.
The experimental probability of rolling a 3 (0.1556) is less than the theoretical probability (0.1667).

Given this information, we can conclude the following:
- The relative frequency of rolling a 4 is [tex]\(\frac{2}{9}\)[/tex]. This statement is correct.
- The experimental probability of rolling a 3 is approximately 0.1556.
- The theoretical probability of rolling any specific number is approximately 0.1667.
- The experimental probability of rolling a 3 is less than the theoretical probability.

Therefore, based on these steps:
- The statement "The relative frequency of rolling a 4 is [tex]\(\frac{2}{9}\)[/tex]" is correct.
- The statement "The experimental probability of rolling a 3 is greater than the theoretical probability of rolling a 3" is incorrect. The experimental probability is less than the theoretical probability.

Considering all steps and calculations, the correct answer should include the statement about the relative frequency of rolling a 4. There is no option provided that is correct, besides the one about the relative frequency of rolling a 4.