Question

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

number cube
number rolled | 1 | 2 | 3 | 4 | 5 | 6
frequency | 11| 16| 14| 20| 12| 17

which statements below represent the situation? select three options.

• the relative frequency of rolling a 4 is \\(\frac{2}{9}\\).
• the experimental probability of rolling a 3 is greater than the theoretical probability of rolling a 3.
• the experimental probability of rolling a 2 is greater than the theoretical probability of rolling a 2.

Explanation:

To solve this, we first calculate the total number of rolls. The frequencies are \(11\) (for 1), \(16\) (for 2), \(14\) (for 3), \(20\) (for 4), \(12\) (for 5), and \(17\) (for 6).

Step 1: Calculate Total Rolls

\[
\text{Total} = 11 + 16 + 14 + 20 + 12 + 17 = 90
\]

Analyze Each Statement:

1. Relative Frequency of Rolling a 4:

Relative frequency of 4 is \(\frac{\text{Frequency of 4}}{\text{Total}} = \frac{20}{90} = \frac{2}{9}\). So this statement is true.

2. Experimental Probability of Rolling a 3:

Experimental probability of 3 is \(\frac{14}{90} \approx 0.155\). Theoretical probability of rolling a 3 on a fair cube is \(\frac{1}{6} \approx 0.166\). Since \(0.155 < 0.166\), the experimental probability is not greater than theoretical. So this statement is false.

3. Experimental Probability of Rolling a 2:

Experimental probability of 2 is \(\frac{16}{90} \approx 0.177\). Theoretical probability of rolling a 2 is \(\frac{1}{6} \approx 0.166\). Since \(0.177 > 0.166\), the experimental probability is greater than theoretical. So this statement is true.

Final Answer (True Statements):

• The relative frequency of rolling a 4 is \(\frac{2}{9}\).
• The experimental probability of rolling a 2 is greater than the theoretical probability of rolling a 2.

(Note: The second statement about rolling a 3 is false.)

Answer:

To solve this, we first calculate the total number of rolls. The frequencies are \(11\) (for 1), \(16\) (for 2), \(14\) (for 3), \(20\) (for 4), \(12\) (for 5), and \(17\) (for 6).

Step 1: Calculate Total Rolls

\[
\text{Total} = 11 + 16 + 14 + 20 + 12 + 17 = 90
\]

Analyze Each Statement:

1. Relative Frequency of Rolling a 4:

Relative frequency of 4 is \(\frac{\text{Frequency of 4}}{\text{Total}} = \frac{20}{90} = \frac{2}{9}\). So this statement is true.

2. Experimental Probability of Rolling a 3:

Experimental probability of 3 is \(\frac{14}{90} \approx 0.155\). Theoretical probability of rolling a 3 on a fair cube is \(\frac{1}{6} \approx 0.166\). Since \(0.155 < 0.166\), the experimental probability is not greater than theoretical. So this statement is false.

3. Experimental Probability of Rolling a 2:

Experimental probability of 2 is \(\frac{16}{90} \approx 0.177\). Theoretical probability of rolling a 2 is \(\frac{1}{6} \approx 0.166\). Since \(0.177 > 0.166\), the experimental probability is greater than theoretical. So this statement is true.

Final Answer (True Statements):

• The relative frequency of rolling a 4 is \(\frac{2}{9}\).
• The experimental probability of rolling a 2 is greater than the theoretical probability of rolling a 2.

(Note: The second statement about rolling a 3 is false.)