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4.8: Chapter 4 - Key Terms and Symbols

Statistics C1000: Introduction to Statistics · LibreTexts

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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).

    This page titled 4.8: Chapter 4 - Key Terms and Symbols was last modified on Wed, 13 Aug 2025 01:13:58 GMT and is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by Toros Berberyan, Tracy Nguyen, and Alfie Swan.