4.8: Chapter 4 - Key Terms and Symbols

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Toros Berberyan, Tracy Nguyen, and Alfie Swan
Citrus College

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Glossary of Key Terms and Symbols

Key Terms

Combination: A selection of items where the order does not matter.

Combination Rule: The number of ways to choose \(r\) items from \(n\) distinct items without regard to order.

Complementary events: Complementary events are two outcomes of a probability experiment that are the only two possible outcomes and together make up the entire sample space.

Event: a set of certain outcomes of an experiment that you want to have happen.

Event Space: the set of outcomes that make up an event. The symbol is usually a capital letter.

Experiment: an activity or process that will produce specific outcomes.

Factorial: The product of all positive integers up to a number \(n\).

Fundamental Counting Rule (Multiplication Rule): If one event can occur in \( m \) ways and another in \( n \) ways, then both events can occur in \( m \times n \) ways.

Independent events are events where the occurrence of one does not affect the occurrence of the other.

Law of large numbers: a rule in which, as "n" increases, the relative frequency tends towards the actual probability value.

Mutually exclusive events (disjoint) are events with no outcomes in common.

Outcomes: the result of an experiment.

Permutation: An arrangement of items where the order matters.

Permutation Rule (no repetition): The number of ways to arrange \( r \) items from \( n \) distinct items.

Permutation with Repetition: Used when some items are repeated.

Probability: the measure of how likely an event is to occur.

Sample Space: a collection of all possible outcomes of the experiment. It is denoted as SS.

Key Terms

\( _nC_r \) - number of combinations (n choose r).

\( E, X, A, B \) - events (subsets of the sample space).

\( \bar{E} \) - complement of event \( E \).

\( ! \) - factorial symbol (e.g., \( n! \)).

\( n \) - total number of items.

\( n! \) - factorial of \( n \).

\( _nP_r \) - number of permutations (arrangements of \( r \) items from \( n \)).

\( P(E) \) - probability that event \( E \) occurs.

\( P(\bar{E}) \) - probability that event \( E \) does not occur.

\( P(B \mid A) \) - conditional probability of \( B \) given \( A \).

\( r \) - number of items selected.

\( SS \) - sample space (the set of all possible outcomes).

Authors

"4.8: Chapter 4 - Key Terms and Symbols" by Toros Berberyan, Tracy Nguyen, and Alfie Swan is licensed under CC BY 4.0

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