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

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

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

The theoretical and experimental probabilities are opposites.
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 number cube (die) has the numbers 1 through 6. The even numbers on the die are 2, 4, and 6. There are 3 even numbers out of 6 possible outcomes.

The theoretical probability of rolling an even number is:

\[ P(\text{even}) = \frac{\text{Number of even outcomes}}{\text{Total number of outcomes}} = \frac{3}{6} = \frac{1}{2} = 0.5 \]

Experimental Probability:

Sadiq rolled the die 10 times and got an even number 7 times. Thus, the experimental probability is:

\[ P(\text{even, experimental}) = \frac{\text{Number of even outcomes (experimental)}}{\text{Total number of trials}} = \frac{7}{10} = 0.7 \]

Comparison:

  • Theoretical Probability: 0.5
  • Experimental Probability: 0.7

Now we can compare the two probabilities:

  • \(0.7 > 0.5\)

Thus, the experimental probability is greater than the theoretical probability.

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