AP Statistics Unit 4 Vocab

random process

generates outcomes that are determined purely by chance

probability

a number between 0 and 1 that describes the proportion of time the outcome would occur in a very long series of trials

Law of Large Numbers

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

simulation

imitates a random process in such a way that simulated outcomes are consistent with real-world outcomes

probability model

description of a random process that consists of 2 parts

• a list of all possible outcomes

• probability of each outcome

sample space

list of all possible outcomes

event

a subset of the possible outcomes from the sample space of a random process

A valid probability model must have:

• all probs from 0-1

• all possible outcome probs must add up to

• Probability that an event does NOT occur is 1 minus the probability it DOES occur

complement rule

says that P(A°) = 1-P(A) where A° is the complement of event A, that is, the event that A does not occur

mutually exclusive

2 events that have no outcomes in common and so can never occur together

General addition rule

any 2 events resulting from the same random process…PIA or B)= P(A) + P(B) - P(A and B)

P(A and B) can be zero for mutually exclusive events

Venn Diagram

one or more circles surrounded by a rectangle

• each circle represents an event

• region inside the rectangle represents the sample space of the random process

Intersection

The event “A and B” of events 

A∩B

Union

The event “A or B” of events

A∪B

conditional probability

the probability that one event happens given that another event is known to happen

Conditional Probability Formula

P(A and B)/P(B)

independent events

knowing whether or not one event has occurred does not change the probability that the other event will happen

General Multiplication Rule

for any random process, the probability that events A and B both occur

tree diagram

shows the sample of a random process involving multiple stages

The probability of each outcome is shown on the corresponding branch of the tree

Multiplication Rule for Independent events

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

P(A) x P(B) = P(A and B)

Applies ONLY to independent events