Question

A number cube was rolled as part of an experiment. The results are in the table below. The fraction StartFraction 1 over x EndFraction is the experimental probability of rolling a 3. What is x?

Experiment Results
Number
1
2
3
4
5
6
Frequency
4
6
5
7
3
5


2
3
5
6

Answer 1

To find the value of \( x \) in the fraction \(\frac{1}{x}\), which represents the experimental probability of rolling a 3, we first need to determine the total frequency of rolls and the frequency of rolling a 3.

From the given frequency table:

- Frequency of rolling 1: 4
- Frequency of rolling 2: 6
- Frequency of rolling 3: 5
- Frequency of rolling 4: 7
- Frequency of rolling 5: 3
- Frequency of rolling 6: 5

First, let's calculate the total number of rolls (total frequency):

\[
\text{Total frequency} = 4 + 6 + 5 + 7 + 3 + 5 = 30
\]

Next, we find the frequency of rolling a 3, which is 5.

The experimental probability of rolling a 3 is given by the formula:

\[
\text{Probability of rolling a 3} = \frac{\text{Frequency of rolling a 3}}{\text{Total frequency}} = \frac{5}{30} = \frac{1}{6}
\]

According to the problem, this probability can also be expressed as \(\frac{1}{x}\). Therefore, we set the two expressions equal:

\[
\frac{1}{x} = \frac{1}{6}
\]

From this, we can see that \( x = 6 \).

Thus, the value of \( x \) is:

\[
\boxed{6}
\]