Question 1

Which of the following best describes a truly random process?

Accepted Answer

A process with no predictable pattern, often simulated using devices like coin flips or random number tables.

Question 2

Why are computers or random number tables often used in statistical experiments?

Accepted Answer

Because they can simulate randomness more reliably than humans.

Question 3

Suppose you toss a coin 10 times and get 7 heads. What is the empirical probability of getting heads?

Accepted Answer

$$0.70$$

Question 4

Which of the following statements about theoretical probability is correct?

Accepted Answer

It is the probability calculated based on theory, assuming infinite repetitions.

Question 5

A simulation is used to estimate the probability of rain on a given day. Which approach to probability does this represent?

Accepted Answer

Simulation-based probability

Question 6

If you flip a fair coin infinitely many times, what is the theoretical probability of getting heads?

Accepted Answer

$$0.50$$

Question 7

Which of the following is a reason to use empirical probability instead of theoretical probability?

Accepted Answer

The theoretical model may be based on faulty assumptions.

Question 8

A student uses a random number table to simulate 20 coin tosses. If 12 of the tosses are heads, what is the empirical probability of heads?

Accepted Answer

$$0.60$$

Question 9

Which of the following best distinguishes empirical probability from theoretical probability?

Accepted Answer

Empirical probability is based on actual experiments, while theoretical probability is based on mathematical reasoning.

Question 10

Why might a simulation be used instead of a real-life experiment?

Accepted Answer

Real-life experiments may be too expensive or time-consuming.

Question 11

If a simulation is designed to closely match a real-life process, what can the results be used for?

Accepted Answer

To estimate empirical probabilities as if they were from real experiments.

Question 12

A researcher flips a coin 100 times and observes 48 heads. What is the empirical probability of heads?

Accepted Answer

$$0.48$$

Question 13

Which of the following is NOT a reason why theoretical, empirical, and simulation-based probabilities are all useful?

Accepted Answer

Theoretical probabilities are always impossible to calculate.

Question 14

If you toss a coin 10 times and get 3 heads, what is the empirical probability of heads?

Accepted Answer

$$0.30$$

Question 15

Which of the following is an example of using simulation-based probability?

Accepted Answer

Using a computer to model the spread of a disease in a population.

Modeling Variation with Probability: Randomness and Probability Approaches

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