Question

Sadiq rolls a regular six-sided number cube 10 times and gets an even number 7 times. How does this experimental probability compare to the theoretical probability?

a. The theoretical probability is greater than the experimental probability
b. The experimental and theoretical probability are equal
c. The theoretical and experimental probabilities are opposites
d. The experimental probability was greater than the theoretical probability

Answer 1

To determine the answer, we need to calculate both the theoretical and experimental probabilities.

1. **Theoretical Probability**: A regular six-sided die (or number cube) has three even numbers: 2, 4, and 6. There are a total of 6 possible outcomes when rolling the die.

\[
\text{Theoretical probability of rolling an even number} = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{3}{6} = \frac{1}{2}
\]

2. **Experimental Probability**: Sadiq rolls the die 10 times and gets an even number 7 times. Thus, the experimental probability is calculated as follows:

\[
\text{Experimental probability of rolling an even number} = \frac{\text{Number of times even number is rolled}}{\text{Total rolls}} = \frac{7}{10}
\]

3. **Comparison**:
- The theoretical probability is \(\frac{1}{2} = 0.5\).
- The experimental probability is \(\frac{7}{10} = 0.7\).

Since \(0.7\) (experimental probability) is greater than \(0.5\) (theoretical probability), the correct comparison is:

**d. The experimental probability was greater than the theoretical probability.**