Chapter 4: Probability and Counting Rules

A set of vocabulary flashcards defining key terms, probability types, event relationships, and counting rules from Chapter 4.

Probability

The chance of an event occurring, which can be used to quantify what the odds are that a specific event will occur.

Probability Experiment

A chance process that leads to well-defined results called outcomes.

Outcome

The result of a single trial of a probability experiment.

Sample Space

The set of all possible outcomes of a probability experiment.

Simple Event

An event with ONE outcome, such as rolling a die and obtaining a three.

Compound Event

An event that may consist of two or more outcomes, such as rolling a die and obtaining an even number.

Classical Probability

A type of probability that uses sample spaces to determine the numerical probability that an event will happen and assumes that all outcomes in the sample space are equally likely to occur.

Equally Likely Events

Events that have the same probability of occurring.

Complement of an Event

The set of outcomes in the sample space that are not included in the outcomes of event $E$, denoted as $\overline{E}$, $E'$, or $E^c$.

Empirical Probability

A type of probability that relies on actual experience to determine the likelihood of outcomes, based on observation from a frequency distribution.

Law of Large Numbers

The principle stating that as the number of trials increases, the empirical probability will approach the theoretical probability.

Subjective Probability

A probability value based on an educated guess or estimate, employing opinions and inexact information.

Mutually Exclusive Events

Two events that cannot occur at the same time, also referred to as disjoint events.

Union of Two Events

The probability of event $A$ OR event $B$ occurring, represented as $P(A \cup B) = P(A \text{ or } B)$.

Intersection of Two Events

The probability of event $A$ AND event $B$ occurring, represented as $P(A \cap B) = P(A \text{ and } B)$.

Independent Events

Two events $A$ and $B$ in which the fact that event $A$ occurs DOES NOT affect the probability of event $B$ occurring.

Dependent Events

Events where the outcome or occurrence of the first event affects the outcome or occurrence of the second event in such a way that the probability is changed.

Conditional Probability

The probability that event $B$ occurs after event $A$ has already occurred, where event $A$ occurs first and event $B$ occurs second, calculated as $P(B|A) = \frac{P(A \cap B)}{P(A)}$.

Fundamental Counting Rule

A rule stating that in a sequence of $n$ events in which the first has $k_1$ possibilities, the second has $k_2$ possibilities, the third has $k_3$ possibilities, and so forth, the total number of possibilities is $k_1 \times k_2 \times k_3 \times \dots \times k_n$.

Combination Rule

A rule used to find the number of ways $r$ objects can be selected from $n$ objects without regard to order, given by $\binom{n}{r} = \frac{n!}{(n - r)! r!}$.