AP Statistics Unit 4: Mastering Probability Rules

Probability

The long-term relative frequency of an event.

Simulation

A method used to estimate probabilities when theoretical calculations are difficult.

Law of Large Numbers

States that as the number of repetitions increases, the proportion of outcomes approaches true probability.

Mutually Exclusive Events

Events that cannot happen at the same time.

Addition Rule

Formula to find the probability that at least one of two events occurs.

$P(A all B)$

Probability of A OR B (Union).

$P(A f B)$

Probability of A AND B (Intersection).

Conditional Probability

The probability of an event given that another event has occurred.

$P(A|B)$

Probability of A given B.

Independent Events

Events where the occurrence of one does not affect the other.

Disjoint Events

Another term for mutually exclusive events; they cannot occur together.

Venn Diagram

A visual representation of relationships among sets.

$P(A ext{ given } B)$

$P(A|B) = \frac{P(A \cap B)}{P(B)}$.

General Multiplication Rule

$P(A f B) = P(A) \cdot P(B|A)$.

Tree Diagram

A diagram used to visualize probabilities of multi-stage experiments.

At Least One Rule

A shortcut for calculating the probability of at least one success.

Complement

The probability of an event not occurring, denoted as $A^C$.

$1-P(A)$

Formula to find the probability of the complement of event A.

Sampling without replacement

A selection method where selected items are not returned to the pool.

Success

In a simulation, the outcome that fulfills the desired condition.

Failure

In a simulation, the outcome that does not fulfill the desired condition.

Double-counting

Adding probabilities that include common outcomes more than once.

Remedial Action

Steps needed to correct miscounted probabilities in calculations.

Exact Probabilities

The theoretical calculation of probabilities based on known values.

Empirical Probabilities

Probabilities estimated based on simulations or observations.

Extreme Events

Outcomes that are unlikely but possible, affecting overall probability.

Estimation Error

The difference between the estimated probability from simulation and the true probability.