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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.


Sagot :

To address the various questions about Nathan's number cube rolls, let's investigate the situation step-by-step.

1. Frequencies of Each Number Rolled:
- 1: 11 times
- 2: 16 times
- 3: 14 times
- 4: 20 times
- 5: 12 times
- 6: 17 times

2. Total Number of Rolls:
- The total number of rolls can be calculated by summing the frequency of each number.
[tex]\[ \text{Total rolls} = 11 + 16 + 14 + 20 + 12 + 17 = 90 \][/tex]

3. Relative Frequency of Rolling a 4:
- The relative frequency is the ratio of the number of times the event occurs to the total number of trials.
[tex]\[ \text{Relative frequency of rolling a 4} = \frac{\text{Frequency of 4}}{\text{Total rolls}} = \frac{20}{90} = \frac{2}{9} \approx 0.2222 \][/tex]

4. Experimental Probability of Rolling a 3:
- The experimental probability is the ratio of the number of times the specific outcome occurs to the total number of trials.
[tex]\[ \text{Experimental probability of rolling a 3} = \frac{\text{Frequency of 3}}{\text{Total rolls}} = \frac{14}{90} \approx 0.1556 \][/tex]

5. Theoretical Probability of Rolling Any Specific Number on a Fair Die:
- Since the number cube is fair, each outcome has an equal chance of occurring.
[tex]\[ \text{Theoretical probability of rolling a 3} = \frac{1}{6} \approx 0.1667 \][/tex]

6. Comparison of Statements:

- Relative Frequency of Rolling a 4 is [tex]\( \frac{2}{9} \)[/tex]:
[tex]\[ \frac{20}{90} = \frac{2}{9} \text{, which is true.} \][/tex]

- Experimental Probability of Rolling a 3 is Greater than the Theoretical Probability of Rolling a 3:
[tex]\[ 0.1556 \not> 0.1667 \text{, which is false.} \][/tex]

Considering the detailed mathematical process and the results obtained, the correct statements related to this situation are:
1. The relative frequency of rolling a 4 is [tex]\( \frac{2}{9} \)[/tex].

The other statement mentioned (Experimental probability of rolling a 3 is greater than the theoretical probability of rolling a 3) is false. Therefore, only one of the given options accurately represents the situation.