AP Statistics Practice Quiz: Estimating Probabilities Using Simulation
Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026
Test your understanding with short quizzes. This quiz has 14 questions to check your progress.
Question 1 of 14
All Questions (14)
A) A process with a predictable, predetermined result.
B) A process where results are determined by chance.
C) A collection of specific outcomes.
D) A model used to estimate probabilities.
Correct Answer: B
Based on the provided content, 'A random process generates results determined by chance.'
A) To determine the true probability of an event with certainty.
B) To model random events in order to estimate their probabilities.
C) To list every possible outcome of a random process.
D) To prove that an event is not random.
Correct Answer: B
The text states, 'Simulation is a way to model random events,' and its purpose is to use the results to estimate probabilities.
A) An event
B) A simulation
C) An outcome
D) A random process
Correct Answer: C
The content defines an outcome as 'the result of a trial of a random process.' Rolling a '4' is the specific result of the single trial (the roll).
A) The single outcome of flipping Heads, Tails, Heads (HTH).
B) The collection of outcomes: {HHT, HTH, THH, HHH}.
C) The random process of flipping a coin three times.
D) The law of large numbers.
Correct Answer: B
The content states that 'An event is a collection of outcomes.' The event 'getting at least two heads' includes all possible outcomes that satisfy this condition.
A) 0.35
B) 0.50
C) 0.65
D) 1.30
Correct Answer: C
The content states that 'The relative frequency of an event in a simulation can be used to estimate its probability.' The relative frequency is the number of times the event occurred (130) divided by the total number of trials (200), which is 130/200 = 0.65.
A) It becomes more random and less predictable.
B) It tends to get closer to the true probability of the event.
C) It will always be equal to exactly 0.5.
D) It will decrease, regardless of the event.
Correct Answer: B
The provided content explicitly states, 'The law of large numbers states that empirical probabilities approach true probabilities as the number of trials increases.'
A) Student A's estimated probability will be closer to the true probability (0.5) than Student B's.
B) Student B's estimated probability will be closer to the true probability (0.5) than Student A's.
C) Both students will get an estimated probability of exactly 0.5.
D) Student A and Student B will have identical estimated probabilities.
Correct Answer: B
The law of large numbers states that as the number of trials increases, the empirical (estimated) probability will get closer to the true probability. Since Student B performed significantly more trials, their estimate is more likely to be accurate.
A) An event
B) A simulation
C) A random process
D) An outcome
Correct Answer: D
The content defines an outcome as 'the result of a trial of a random process.' The number '2' is the specific result from a single trial (the computer generating a number).
A) 0.250
B) 0.370
C) 0.500
D) 2.700
Correct Answer: B
The empirical probability is estimated using the relative frequency from the simulation. This is calculated as the number of times the event occurred (185) divided by the total number of trials (500), which is 185/500 = 0.37.
A) The simulation was not a random process.
B) The number of trials is too small for the law of large numbers to suggest the estimate is close to the true probability.
C) An event cannot be a collection of outcomes.
D) The relative frequency can only be calculated with more than 100 trials.
Correct Answer: B
The law of large numbers states that the empirical probability approaches the true probability as the number of trials increases. With only 15 trials, the result is highly subject to chance variation and may not be close to the true probability.
A) The result of a single trial of a random process.
B) A process where results are determined by chance.
C) A collection of one or more outcomes.
D) A model used to represent a random process.
Correct Answer: C
The provided content explicitly states that 'An event is a collection of outcomes.'
A) The simulation is flawed because the result (0.636) is not equal to the individual defect rate (0.02).
B) The true probability of finding at least one defective chip in a box of 50 is likely close to 0.636.
C) The simulation needs fewer trials to be accurate.
D) The random process of a chip being defective is not actually random.
Correct Answer: B
Due to the very large number of trials (500,000), the law of large numbers implies that the empirical probability (relative frequency) of 0.636 is a very good estimate of the true probability for the specified event (at least one defect in 50).
A) Calculating the sales tax on a $50 purchase.
B) Flipping a fair coin.
C) Following a set of instructions to assemble furniture.
D) Determining the boiling point of water at sea level.
Correct Answer: B
A random process generates results determined by chance. Flipping a coin has a chance-based result. The other options have predetermined, calculated results.
A) Roll a six-sided die twice. A roll of 1, 2, 3, or 4 means a correct answer.
B) Flip a coin twice. Heads means correct, tails means incorrect.
C) Use a random number generator to pick two integers from 1 to 4. For each integer, a 1, 2, or 3 represents a correct answer.
D) Use a random number generator to pick one integer from 1 to 4. A 1, 2, or 3 means both answers were correct.
Correct Answer: C
This simulation correctly models the random process for each of the two questions. It uses a 3/4 = 75% chance for a correct answer and repeats it twice to simulate the event. Option A has the wrong probability (4/6 ≈ 67%). Option B has the wrong probability (50%). Option D incorrectly models only one event for the two questions instead of two separate events.