Statistics 4.1 Introduction to Probability

Questions and Answers

What is a probability experiment?

A process in which the result is random in nature, such as flipping a coin or tossing dice.

What is an outcome in a probability experiment?

An individual result from a probability experiment.

What is meant by the sample space in probability?

The set of all possible outcomes for a given probability experiment.

Define an event in the context of probability.

A subset of outcomes of the sample space. Signup and view all the answers

What is a tree diagram?

A method that organizes outcomes in a systematic manner. Signup and view all the answers

What is subjective probability?

An educated guess regarding the chance that an event will occur. Signup and view all the answers

What is empirical (or experimental) probability?

The probability found by performing an experiment. Signup and view all the answers

What is the empirical (or experimental) probability formula?

P(E) = f/n where f is the frequency of event E and n is the total number of trials. Signup and view all the answers

What is the rounding rule when calculating probability?

Give the exact fraction or a decimal rounded to four decimal places. Signup and view all the answers

What does the Law of Large Numbers state?

The greater the number of trials, the closer the experimental probability will be to the true probability. Signup and view all the answers

What is classical probability?

The most precise type of probability, calculated by considering all possible outcomes. Signup and view all the answers

What is the classical probability formula?

P(E) = n(E)/n(S) where n(E) is the number of outcomes in the event and n(S) is the number of outcomes in the sample space. Signup and view all the answers

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.