Probability Concepts and Misunderstandings

What is the main claim being tested in the lesson?

• Blowing on a die increases the chance of rolling a four.

• Rolling a die twice increases the chance of a four.

• Rolling a die without blowing increases the chance of a six.

• Blowing on a die decreases the chance of rolling a one.

What does theoretical probability rely on?

• Sample space

• Empirical data

• Number of trials

• Actual experience

What is the probability of landing on heads when flipping a fair coin?

• 0.25 or 25%

• 1 or 100%

• 0.5 or 50%

• 0.75 or 75%

What does empirical probability depend on?

• Actual experience

• Hypothetical scenarios

• Theoretical calculations

• Sample space

According to the law of large numbers, what happens as the number of trials increases?

• Theoretical probability becomes zero

• Empirical probability approaches theoretical probability

• Theoretical probability decreases

• Empirical probability becomes less accurate

What is the theoretical probability of rolling a four on a six-sided die?

• 0.33 or 33%

• 0.25 or 25%

• 0.17 or 17%

• 0.5 or 50%

What is a common misunderstanding about empirical and theoretical probabilities?

• They are never equal

• Theoretical probability is always lower

• Empirical probability is always higher

• They are always equal

In an experiment of 36 rolls, how many times did the die land on four to match the theoretical probability?

• 6 times

• 8 times

• 10 times

• 12 times

What was the empirical probability when the die landed on four 10 times in 36 rolls?

• 33.3%

• 27.8%

• 17%

• 50%

Why can't a small number of trials prove the effect of blowing on a die?

• Small trials always show higher empirical probability

• Small trials are not statistically significant

• Small trials always match theoretical probability

• Small trials are always incorrect