17 terms

Probability

A number between 0 and 1 that describes the proportion of times any outcome of a chance process would occur in a very long series of repetitions.

Law of Large Numbers

If we observe more and more repetitions of any chance process, the proportion of times a specific outcome will occur approaches a single value (in the long run). In the short run, it is unpredictable.

Simulation

An imitation of chance behavior based on a chance model that accurately reflects the situation.

Sample Space (S)

The set of all possible outcomes of a chance process.

Probability Model

A description of some chance process that consists of two parts: a sample space S and a probability for each outcome.

Event

Any collection of outcomes from some chance process. A subset of the sample space. Usually designated by capital letters.

Complement

The scenario where an event does NOT occur. The _______ of event A, is calculated 1 - P(A)

Mutually Exclusive (Disjoint)

Two outcomes that have no outcomes in common so can never occur together. These events can never be independent, because if one can't happen with the other. If one happens, the other can never happen.

Venn Diagram

A way to illustrate the sample space of a chance process including two events, consisting of two circles representing the events.

Intersection (∩)

All the outcomes in common between two events compared. P(A and B)

Union (U)

All the outcomes in the two events included. P(A or B)

General Addition Rule

P(A or B) = P(A) + P(B) - P(A and B)

Fixes the double counting problem because of the overlapping outcomes.

Fixes the double counting problem because of the overlapping outcomes.

Conditional Probability

The probability an event will occur given another event has already occurred. Denoted by P(B|A).

P(B|A) = P(A∩B)/P(B)

P(A|B) = P(B∩A)/P(A)

P(B|A) = P(A∩B)/P(B)

P(A|B) = P(B∩A)/P(A)

Independent Events

Two events in which the occurrence of one event does not change the probability that the other with happen. P(A|B) = P(A), and P(B|A) = P(B)

General Multiplication Rule

Finds the probability both A and B occur using the formula:

P(A and B) = P(A∩B) = P(A) * P(B|A)

P(A and B) = P(A∩B) = P(A) * P(B|A)

Tree Diagram

Displays the sample space of a process involving a sequence of events, with each each subsequent event branching out from the first like a tree.

Multiplication Rule for Independent Events

If A and B are independent, probability A and B both occur is:

P(A∩B) = P(A) * P(B)

P(A∩B) = P(A) * P(B)