Statistics 4.1 Introduction to Probability

Study Notes

Probability Concepts

Probability Experiment (Trial): A process yielding random results, examples include flipping a coin, rolling dice, and drawing raffle tickets.
Outcome: The individual result derived from a probability experiment, such as heads or tails from a coin flip.
Sample Space: The complete set of all possible outcomes for a given probability experiment.
Event: A subset of outcomes from the sample space, which can also represent the entire sample space.

Visual and Calculation Tools

Tree Diagram: A visual representation that systematically organizes the outcomes of a probability experiment.
Subjective Probability: An educated estimate regarding the likelihood of an event occurring, influenced by the estimator's expertise.
Empirical (Experimental) Probability: Determined by conducting an experiment; calculated by dividing the frequency an event occurs by the total trials performed.

Probability Formulas

Empirical Probability Formula: P(E) = f/n, where P(E) is the probability of event E, f is the frequency of event E, and n is the total number of trials.
Rounding Rule for Probability: Probabilities can be expressed as exact fractions or decimals rounded to four decimal places. Very small probabilities may be rounded to the first nonzero digit.
Law of Large Numbers: As the number of trials increases, the experimental probability approaches the true probability.
Classical Probability (Theoretical Probability): The most precise form of probability, based on all possible outcomes, computed for equally likely outcomes.

Classical Probability Formula

Classical Probability Formula: P(E) = n(E)/n(S), where P(E) is the probability of event E, n(E) is the number of outcomes in event E, and n(S) is the total number of outcomes in the sample space.

Description

Test your knowledge of fundamental concepts in probability with these flashcards. Explore terms like probability experiment, outcome, and sample space to solidify your understanding of randomness in experiments. Perfect for beginners in statistics or those reviewing for exams.