AP Stats chapter 5

Random Process

A(n) ______ generates outcomes that are determined purely by chance.

Probability

A(n) ______ of any outcome of a random process is a number between 0 and 1 that describes the proportion of times the outcome would occur in a very long series of trials.

Law of Large Numbers

The ______ says that if we observe more and more trials of any random process, the proportion of times that a specific outcome occurs approaches its probability.

Simulation

A(n) ______ imitates a random process in such a way that simulated outcomes are consistent with real-world outcomes.

simulation process

The _______:
- Describe how to use a random process to perform one trial of the simulation. Tell what you will record at the end of each trial.
- Perform many trials of the simulation.
- Use the results of your simulation to answer the question of interest.

probability model

A(n) ______ is a description of some random process that consists of two parts: a list of all possible outcomes and the probability for each outcome.

Sample Space

The list of all possible outcomes is called the ______

event

A(n) ______ is any collection of outcomes from some random process.

complement rule, complement

The _______ says that P(AC)= 1 - P(A), where AC is the _______of event A; that is, the event that A does not occur. Other common notation is A'

mutually exclusive (disjoint)

Two events A and B are ______ if they have no outcomes in common and so can never occur together - that is, if P(A and B) = 0.

P(A and B) = 0

Mutually Exclusive notation

addition rule for mutually exclusive events

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

general addition rule

If A and B are any two events resulting from some random process, the ______ says that P(A or B) = P(A) + P(B) - P(A and B) *be sure to always show work when doing these calculations.

Venn Diagram

A(n) ______ consists of one or more circles surrounded by a rectangle. Each circle represents an event. The region inside the rectangle represents the sample space of the random process.

Intersection

The event "A and B" is called the ______ of events A and B. It consists of all outcomes that are common to both events, and is denoted A ∩ B * ∩ for intersection.

A ∩ B

Intersection, A and B (notation)

Union

The event "A or B" is called the ______ of events A and B. It consists of all outcomes that are in event A or event B, or both, and is denoted A ∪ B. * ∪ for union.

A ∪ B.

Union, A or B (notation)

conditional probability

the probability that one event happens given that another event is already known to have happened is called a(n) ______

Conditional Probability notation

P(A|B)

Calculationg Conditional Probability

Probability of A and B divided by the probability of B

independent events

A and B are ______ if knowing whether or not one event has occurred does not change the probability that the other event will happen.

P(A|B) = P(A|Bc) = P(A)

Independent event form (reversible)

General Multiplication Rule

For any random process, the probability that events A and B both occur can be found using the ______

General Multiplication Rule form

P(A and B) = P(A ∩ B) = P(A) x P(B|A) *note: P(B|A) = P(B ∩ A)/P(A)

tree diagram

A(n) ______ shows the sample space of a random process involving multiple stages. The probability of each outcome is shown on the corresponding branch of a tree. All probabilities after the first stage are conditional probabilities.

P(A) x P(B)

If A and B are independent events, the probability that A and B both occur is