Statistics Section 3 Flashcards

Key Concepts in Probability

• Random Experiment: An action resulting in one of several possible outcomes that cannot be predicted with certainty.

• Classical Approach to Probability: Assumes all outcomes are equally likely; for example, rolling a fair die gives each of the six faces a probability of 1/6.

• Relative Frequency Approach: Estimates probability based on the long-term frequency of an outcome; for instance, if 200 out of 1000 students receive an A, the relative frequency is 20%.

• Subjective Approach: Involves personal judgment and belief; an example includes weather forecasting, which combines previous data and current observations.

Types of Probability

• Joint Probability: The probability of two events occurring simultaneously; it represents the intersection of those events.

• Marginal Probability: Evaluates the likelihood of an event occurring without consideration of other events; it measures standalone probabilities.

• Conditional Probability: The likelihood of one event occurring given that another has occurred; crucial for understanding dependent events.

Events and Their Relationships

• Union of Two Events: Refers to the event consisting of all outcomes found in either event A or event B or both.

• Complement of Event A: Represents outcomes where A does not happen; the sum of the probabilities of an event and its complement equals 1.

Advanced Probability Concepts

• Bayes' Law: A formula used to calculate posterior probabilities, allowing for the update of the probability estimate based on new evidence.

• Proportional Expectation in Classical Approach: Describes probability in terms of how often an outcome is expected to occur theoretically over numerous trials.

• Exhaustive Events: A set of events that includes all possible outcomes of an experiment, providing complete coverage for probability assessments.

Rules and Classifications

• Addition Rule: For mutually exclusive events, the probability that one or the other occurs is the sum of their individual probabilities.

• Mutually Exclusive Events: Events that cannot occur at the same time; the occurrence of one excludes the others.