Question

Quinta is rolling a dice and keeping track of the number she gets on each roll. The table below summarizes her results.

Rolling a Dice
Number Frequency
1 15
2 17
3 14
4 16
5 15
6 14


What are the experimental and theoretical probabilities of rolling the number 4? Round your answer to the nearest thousandth.

Experimental probability


Theoretical probability

Answer 1

To find the experimental and theoretical probabilities of rolling the number 4, we need to understand both concepts:

1. **Experimental Probability**: This is calculated based on the results of the actual rolls of the dice. The formula for experimental probability is:

\[
P(E) = \frac{\text{Number of times the event occurs}}{\text{Total number of trials}}
\]

2. **Theoretical Probability**: This is based on what we expect to happen in a perfect scenario. For a fair dice, the theoretical probability of rolling any specific number (like 4) is:

\[
P(E) = \frac{1}{6}
\]

Now let’s calculate both probabilities for the number 4:

### 1. Experimental Probability of Rolling a 4:

From the table, the frequency of rolling a 4 is 16. We can calculate the total number of rolls by adding up the frequencies for all numbers:

\[
\text{Total Rolls} = 15 + 17 + 14 + 16 + 15 + 14 = 91
\]

Now, we can find the experimental probability of rolling a 4:

\[
P(\text{rolling a 4}) = \frac{16}{91} \approx 0.1758
\]

Rounding to the nearest thousandth, the experimental probability is:

\[
P(\text{rolling a 4}) \approx 0.176
\]

### 2. Theoretical Probability of Rolling a 4:

For a fair six-sided dice, the theoretical probability of rolling a 4 is:

\[
P(\text{rolling a 4}) = \frac{1}{6} \approx 0.1667
\]

Rounding to the nearest thousandth, the theoretical probability is:

\[
P(\text{rolling a 4}) \approx 0.167
\]

### Summary:
- **Experimental Probability of rolling a 4**: 0.176
- **Theoretical Probability of rolling a 4**: 0.167