Question

when would you expect the experimental probability of an event to be closest to its theoretical probability?
a. when the results of 10 trials were used in calculating the theoretical probability
c. when the results of 100 trials were used in calculating the experimental probability
b. when the results of 10 trials were used in calculating the experimental probability
d. none of the above, because the experimental probability is unrelated to the theoretical probability.
please select the best answer from the choices provided

Explanation:

To determine when experimental probability is closest to theoretical probability, we use the law of large numbers: as the number of trials (n) increases, experimental probability approaches theoretical probability.

• Option a: Theoretical probability is calculated using formulas, not trial results, so a is incorrect.
• Option b: 10 trials are a small sample, so experimental probability won’t be close to theoretical.
• Option c: 100 trials are more than 10, so the experimental probability (from more trials) will be closer to theoretical.
• Option d: Experimental and theoretical probabilities are related (experimental approaches theoretical with more trials), so d is incorrect.

Answer:

C. When the results of 100 trials were used in calculating the experimental probability