Unit 12 Algebra 2 Probability Flashcards

Questions and Answers

Match the following terms with their definitions:

Experiment = Some process that occurs with well defined outcomes. Outcome = A result from a single trial of the experiment. Event = A collection of one or more outcomes. Sample Space = A collection of ALL outcomes of an experiment.

What is the basic definition of probability?

P(E) = n(E) / n(S)

Theoretical probability requires running an experiment to determine the probability of an event.

False

What does empirical probability involve?

Quantifying probability by using observed data. Signup and view all the answers

What does Union represent in probability?

A or B = A⋃B = {x: x is in A or x is in B} Signup and view all the answers

What does Intersection represent in probability?

A and B = A⋂B = {x: x is in A and x is in B} Signup and view all the answers

What is the Probability of Addition Rule?

P(A or B) = P(A) + P(B) − P(A and B) Signup and view all the answers

What is Conditional Probability?

Probability of one event occurring changes depending on other events occurring. Signup and view all the answers

In dependent events, the outcome of the first event does not affect the second.

False Signup and view all the answers

In independent events, the fact that A occurs does not affect the probability of B occurring.

True Signup and view all the answers

What is the Multiplication Property of Probability?

P(A and B) = P(A) * P(B) Signup and view all the answers

Study Notes

Key Concepts in Probability

Experiment: A process with well-defined outcomes where observations can be made.
Outcome: The result of a single trial within an experiment, providing specific information about that instance.
Event: A set or collection of one or more outcomes from an experiment, focusing on particular results.
Sample Space: Represents the complete collection of all possible outcomes from an experiment, serving as the foundation for probability calculations.

Definitions and Formulas

Basic Definition of Probability: Expressed as P(E) = n(E) / n(S), where n(E) is the number of favorable outcomes and n(S) is the total number of outcomes in the sample space.
Theoretical Probability: Determined without conducting experiments, relying on known outcomes and properties instead.
Empirical Probability: Based on actual observations and experiments, used to estimate the likelihood of events.

Set Operations in Probability

Union: Denoted as A ∪ B; represents the collection of outcomes that belong to either event A or event B.
Intersection: Denoted as A ∩ B; captures outcomes common to both events A and B.

Addition and Conditional Probability

Probability of Addition Rule: P(A or B) = P(A) + P(B) − P(A and B); this formula accounts for the overlap between events A and B.
Conditional Probability: The probability of an event depends on the occurrence of one or more other events, reflecting a dependency in outcomes.

Types of Dependencies

Dependent Events: The outcome of one event influences the outcome of a second event, indicating a connection between events.
Independent Events: The occurrence of one event has no effect on the probability of the second event occurring, maintaining distinct probabilities.

Multiplication Property

Multiplication Property of Probability: For independent events, P(A and B) = P(A) * P(B), reflecting the combined probability of two events happening together.

Description

Test your knowledge of key concepts in probability with these matching flashcards from Unit 12 of Common Core Algebra 2. Each card presents essential definitions and terms such as experiment, outcome, and sample space. Challenge yourself to match the words with their correct meanings!