Introduction to Probability - AP Statistics

$\frac{1}{3}$. Numbers 5 and 6 out of six possibilities.

Probability is the measure of the likelihood of an event occurring. Quantifies the likelihood on a scale from 0 to 1.

Probability values range from 0 to 1. 0 means impossible, 1 means certain.

The probability of an impossible event is 0. An event that cannot occur has zero probability.

The probability of a certain event is 1. An event that must occur has probability 1.

$P(E') = 1 - P(E)$. Complement probability equals 1 minus the event probability.

$P(A \text{ or } B) = P(A) + P(B)$. For mutually exclusive events, probabilities simply add.

$P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)$. Subtracts overlap to avoid double-counting.

$P(A \text{ and } B) = P(A) \times P(B)$. For independent events, multiply individual probabilities.

Conditional probability is the probability of an event given another event. Probability of one event assuming another has occurred.

$P(A|B) = \frac{P(A \text{ and } B)}{P(B)}$. Divides joint probability by the given event's probability.

$P(A \text{ and } B) = P(A) \times P(B|A)$. Multiplies probability of first by conditional probability.

Events $A$ and $B$ are independent. When conditional equals marginal probability, events are independent.

$P(A \text{ or } B) = P(A) + P(B)$. Mutually exclusive means no overlap, so probabilities add.

Joint probability. Describes the probability of both events occurring together.

The sample space is the set of all possible outcomes. Contains every possible outcome of an experiment.

Mutually exclusive events cannot occur at the same time. Events with no shared outcomes.

$P(A') = 0.3$. Using complement rule: $1 - 0.7 = 0.3$.

$A \text{ and } B$. Intersection notation for events occurring together.

$\frac{1}{4}$ or 0.25. 13 hearts out of 52 total cards.

$\frac{1}{6}$. One favorable outcome out of six possible.

An outcome is a possible result of a probability experiment. A single possible result from an experiment.

$\frac{1}{2}$. Three even numbers (2, 4, 6) out of six total.

An event is a set of outcomes from a probability experiment. A collection of one or more outcomes.

Complement of event $E$. Standard notation for the complement of event E.

$\frac{1}{13}$. Four aces in a standard 52-card deck.

$P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)$. General addition rule accounting for overlap.

$\frac{1}{2}$. 26 red cards (hearts and diamonds) out of 52.

A probability distribution lists all the possible outcomes and their probabilities. Maps each outcome to its probability value.