Math 1332 Chapter 11 - Unit 2 Review

Vocabulary flashcards covering core probability, counting principles, permutations, expected value, and conditional probability concepts from Math 1332 Chapter 11 (Unit 2 Review).

Odds Against an Event

The ratio of the probability that an event does not occur to the probability that the event does occur, represented as $P(\text{not } E) : P(E)$ or $\frac{P(E')}{P(E)}$.

Addition Rule for Probability

A rule stating that the probability of event $A$ or event $B$ occurring is the sum of their individual probabilities minus the probability of both occurring together: $P(A \cup B) = P(A) + P(B) - P(A \cap B)$.

Sample Space

The complete set of all possible outcomes resulting from a probability experiment, such as the $2^4 = 16$ gender sequences for a family with four children.

Tree Diagram

A branching graphical model used to trace and list all possible sequential outcomes in a multi-stage experiment.

Distinguishable Permutations

The number of distinct arrangements of $n$ items where some items are repeated, calculated using the formula $\frac{n!}{n_1! \, n_2! \, \cdots \, n_k!}$, where each $n_i$ represents the frequency of an identical element.

Sampling Without Replacement

A selection process in which items are removed from a population and not returned, causing the total number of items and the probability of subsequent selections to change after each draw.

Face Card

Any card in a standard 52-card deck depicting an individual—namely a Jack, Queen, or King—amounting to 12 total cards across all four suits.

Expected Value

The theoretical long-run weighted average outcome of a random variable, calculated by multiplying each possible numerical outcome by its corresponding probability and summing the results: $E = \sum [x \times P(x)]$.

Fair Game

A game or wager whose expected monetary value is exactly zero ($E = \$0$), meaning that on average neither the player nor the house possesses a statistical advantage.

Fundamental Counting Principle

A multiplication rule establishing that if an event can occur in $m$ ways and a second independent event can occur in $n$ ways, the sequence of both events can occur in $m \times n$ total ways.

Conditional Probability

The probability that event $A$ will occur given the knowledge that event $B$ has already occurred, denoted as $P(A|B) = \frac{P(A \cap B)}{P(B)}$.

Contingency Table

A two-way frequency table showing the joint distribution of two categorical variables across rows and columns, used to calculate marginal, joint, and conditional probabilities.