Explain discrepancies in results from a probability model by comparing the experimental and theoretical probabilities

The video tutorial explains discrepancies between experimental and theoretical probabilities, emphasizing the law of large numbers. It highlights common mistakes, such as assuming experimental probabilities will equal theoretical ones with enough trials. Chris's experiment is analyzed to show how experimental probabilities approach theoretical values with more trials. The video also discusses how large sample spaces require more trials to achieve accurate experimental probabilities.

What does the law of large numbers suggest about experimental probabilities?

• They will always equal theoretical probabilities.

• They will decrease as the number of trials increases.

• They will get closer to theoretical probabilities with more trials.

• They will become more random with more trials.

Why is it unlikely for experimental probabilities to equal theoretical probabilities?

• Because theoretical probabilities are based on incorrect assumptions.

• Because experimental probabilities are subject to chance and variability.

• Because theoretical probabilities are always changing.

• Because experimental probabilities are fixed.

In Chris's experiment, what was the theoretical probability of rolling a four?

• 1/3

• 1/4

• 1/6

• 1/2

What is one reason why experimental probabilities might not match theoretical probabilities?

• The theoretical probability is incorrect.

• The number of trials is too few.

• The experimental setup is flawed.

• The sample space is too small.

How can a large sample space affect experimental probabilities?

• It has no effect on the accuracy of experimental probabilities.

• It necessitates a large number of trials to approach theoretical probabilities.

• It requires fewer trials to achieve accurate results.

• It makes it easier to match theoretical probabilities.