Question

experimental vs. theoretical probability
roll the number cube to find the observed frequency
which statements are true? choose two correct answers.
as the number of trials
increases, there is no
change in the
experimental
probabilities.
as the number of trials
increases,
experimental
probability is closer to
theoretical probability.
as the number of trials
increases, there is no
change in the
theoretical
probabilities
as the number of trials
increases, theoretical
probability changes to
more closely match the
experimental
probability.

Explanation:

• Theoretical probability is based on the nature of the event (for a fair number cube, the theoretical probability of each outcome is \(\frac{1}{6}\)).
• Experimental probability is based on the results of trials. As the number of trials increases, according to the law of large numbers, the experimental probability gets closer to the theoretical probability.
• Theoretical probability is a fixed value for a given situation (e.g., for a fair cube, it's always \(\frac{1}{6}\) for each face), so it doesn't change with the number of trials.

Answer:

• The second statement: "As the number of trials increases, experimental probability is closer to theoretical probability."
• The third statement: "As the number of trials increases, there is no change in the theoretical probabilities."