Glossary
Biased chance device
A chance device that does not accurately represent the true probabilities of the outcomes in the random process it is intended to model, leading to skewed results.
Example:
Using a coin that is weighted to land on heads 70% of the time when simulating a fair coin flip would be an example of a biased chance device.
Chance device
A tool or method used in a simulation to imitate the random process being studied, ensuring outcomes are determined by chance.
Example:
In a simulation to model winning a prize with a 20% chance, a random number generator where 0-19 represents a win acts as the chance device.
Event
A collection of one or more specific outcomes from a random process, often defined by a particular characteristic.
Example:
When rolling a die, getting an 'even number' (2, 4, or 6) is an event.
Law of Large Numbers (LLN)
A fundamental principle stating that as the number of trials or repetitions of a random process increases, the observed (empirical) probability of an event will converge towards its true theoretical probability.
Example:
The Law of Large Numbers explains why, after many coin flips, the proportion of heads will get closer and closer to 0.5, even if short runs show deviations.
Outcomes
The result of a single instance or trial of a random process.
Example:
When flipping a coin, getting 'Heads' is an outcome.
Probability
A numerical measure, between 0 and 1, that quantifies the likelihood of an event occurring, representing the long-run proportion of times the event would happen.
Example:
The probability of rolling a 4 on a fair six-sided die is 1/6.
Random processes
Processes where the results or outcomes are determined by chance, meaning their exact outcome cannot be predicted beforehand.
Example:
Rolling a standard six-sided die is a random process because you can't predict which face will land up.
Simulations
A method used to model random events, creating synthetic data based on assumptions to understand patterns and estimate probabilities.
Example:
To estimate the probability of a basketball player making 3 free throws in a row, you could run a simulation by flipping a coin multiple times for each shot.
Trial (Simulation Trial)
A single repetition of a simulation process, designed to imitate one instance of the real-world random event being studied.
Example:
If you're simulating a basketball player making 3 free throws, one sequence of 3 simulated shots (e.g., using random numbers) constitutes a single trial.