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)

Responses

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

The theoretical probability is greater than the experimental probability.
The theoretical probability is greater than the experimental probability.

The experimental and theoretical probability are equal.
The experimental and theoretical probability are equal.

The theoretical and experimental probabilities are opposites.

1 answer

To compare the experimental probability with the theoretical probability, we first need to calculate both.

Theoretical Probability: A regular six-sided die has the numbers 1 through 6. The even numbers on the die are 2, 4, and 6. So, there are 3 even numbers out of 6 total numbers.

The theoretical probability \( P \) of rolling an even number is: \[ P(\text{even}) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{3}{6} = \frac{1}{2} = 0.5 \]

Experimental Probability: Sadiq rolls the die 10 times and gets an even number 7 times. Thus, the experimental probability \( E \) of rolling an even number is: \[ E(\text{even}) = \frac{\text{Number of even outcomes from experiments}}{\text{Total experiments}} = \frac{7}{10} = 0.7 \]

Comparison:

  • Theoretical probability: 0.5
  • Experimental probability: 0.7

Now comparing these:

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

Thus, the correct response is: The experimental probability was greater than the theoretical probability.