AP STATS CH 5

random phenomenon

chance behavior with a regular distribution of outcomes over a LARGE number of trials

probability

P(E) = # of ways desired outcomes occur/ # of total possible outcomes

sample space

all possible outcomes of a random phenomenon

event

specific outcome(s) from the sample space that stratify the desired outcome

simulation

model that mathematically reflects the situation of interest

simulation step 1

state - state question of interest

simulation step 2

plan - describe how to model the situation (1 repetition)

• state assumptions

• assign digits

• describe process

simulation step 3

do - carry out many repetitions and record

simulation step 4

conclude - use results to answer “question of interest”

complement

all outcomes not part of an event, but in the sample space

disjoint (mutually exclusive)

events that have NO COMMON OUTCOMES but are in the sample space

• P(A and B) = 0

• If disjoint, this is true P(A and B) = P(A) + P(B)

independent

knowing an outcome of an event does not impact thee probability of another event

• P(A) = P(A|B)

• if ind basic mult. rule holds: P(A and B) = P(A) * P(B)

value of probability

0 <= P(A) <= 1

total probability

sum of all probabilities of all possible outcomes for a sample space = 1

complement rule

P ( A^c ) = 1 − P ( A )

addition rule

only for disjoint events

• P(A or B) = P(A) + P(B)

multiplication rule

only for independent events

• P(A and B) = P(A) * P(B)

conditional

P(A|B) = A given B

general addition rule

use when not disjoint

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

general multiplication rule

use when not independent

• P(A and B) = P(A) * P(B|A)

conditional probability rule

P(B|A) = P(A and B)/P(A)