Sadiq rolls a regular six-sided number cube 10 times and gets an even number 7 times. How does his experimental probability compare to the theoretical probability? (1 point)

Question

• The theoretical and experimental probabilities are opposites.
The theoretical probability is
• greater than the experimental probability.
The experimental probability was
• greater than the theoretical probability.
• The experimental and theoretical probability are equal.

Answer 1

To determine how Sadiq's experimental probability compares to the theoretical probability, we first need to calculate both.

Theoretical Probability:

For a regular six-sided die, the even numbers are 2, 4, and 6. There are 3 even numbers out of 6 total possible outcomes. So, the theoretical probability of rolling an even number is:

\[ \text{Theoretical Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{3}{6} = \frac{1}{2} = 0.5 \]

Experimental Probability:

Sadiq rolled the die 10 times and got an even number 7 times. The experimental probability of rolling an even number is:

\[ \text{Experimental Probability} = \frac{\text{Number of even rolls}}{\text{Total rolls}} = \frac{7}{10} = 0.7 \]

Comparison:

• Theoretical Probability = 0.5
• Experimental Probability = 0.7

Now, comparing these:

• The theoretical probability (0.5) is less than the experimental probability (0.7).

Therefore, the answer is: The theoretical probability is greater than the experimental probability.