What the exam asks
Expect three core tasks across Section I and Section II:
- Interpret simulation results: Given a dotplot, histogram, or table of 100 to 10,000 simulated trials, estimate the probability of a specified event by counting outcomes and dividing by the total number of trials.
- Design or critique a simulation: Explain how to use a random number generator (RNG), a table of random digits, or physical items (dice, cards, slips of paper) to model a real-world chance process, paying close attention to whether sampling is with or without replacement.
- Apply the Law of Large Numbers (LLN): Interpret probability as a long-run relative frequency and debunk misconceptions about short-run streaks (the “gambler’s fallacy”).
Core ideas
Random processes, outcomes, and events
A random process is a repeatable situation where all possible results are known in advance, but the exact result of any single trial cannot be predicted with certainty.
- Trial: One repetition of the random process.
- Outcome: One possible result of a trial (for example, rolling a 4 on a six-sided die).
- Event: A collection of one or more outcomes of interest (for example, rolling an even number: 2, 4, or 6).
Probability and the Law of Large Numbers
The probability of an event is its long-run relative frequency—the proportion of times the event would occur if the random process were repeated independently an infinite number of times.
The Law of Large Numbers (LLN) states that as the number of independent trials increases, the cumulative relative frequency (empirical proportion) of an event gets closer and closer to a single value: the true theoretical probability.