Question

1. which of the following could explain a discrepancy between theoretical and empirical probability?

a. all of the above
b. small sample size
c. random chance
d. bias in the experiment

Explanation:

• Small sample size: With a small sample, the empirical results may not accurately reflect the theoretical probability. For example, if you flip a coin a few times, you might not get close to the 50 - 50 theoretical probability of heads and tails.
• Random chance: Even with a large sample, random fluctuations can cause a discrepancy. Just because the theoretical probability of an event is a certain value doesn't mean every experiment will yield that exact value due to randomness.
• Bias in the experiment: If the experiment is set up in a way that favors certain outcomes (e.g., a loaded die in a probability experiment about dice rolls), it will create a difference between the theoretical and empirical probability.

Since all of these factors (small sample size, random chance, and bias in the experiment) can cause a discrepancy between theoretical and empirical probability, the option “All of the above” is correct.

Answer:

A. All of the above