Unit three

Probability experiment

an action or trial, through which specific results (counts, measurements, or respones) are obtained

outcome

the result of a single trial in a probability experiment

sample space

the set of al possible outcomes of a probability experiment

event

a subset of the sample space, may consist of one or more outcomes

tree diagram

gives a visual display of the outcomes of a probability experiment by using branches that originate from a starting point, can be used to find the number of possible outcomes in a sample space as well as individual outcomes

simple event

an event that consists of a single outcome

Fundamental counting principle

find the number of ways two or more events can occur in sequence, if one event can occur in m ways and a second event can occur in n ways, then the number of ways the two events can occur in sequence is m x n

classical (or theoretical) probability

used when each outcome in a sample space is equally likely to occur. wants/total

Empirical (or statistical) probability

based on observations obtained from probability experiments, f/n

Law of Large numbers

as an experiment is repeated over and over, the empirical probability (relative frequency) of an event approaches the theoretical (actual) probability of the event

Subjective probability

result from intuition, educated guesses, and estimates

Range of probabilities rule

the probability of an event E is between 0 and 1, inclusive, 0?P(E)?1

complement of event E

the set of all outcomes in a sample space that are not included in event E, (E' E prime)

conditional probability

the probability of an event occurring, given that another event has already occurred. probability of B given A

independent

the occurrence of one of the events does not affect the probability of the occurrence of the other event

Dependent

not independent events

multiplication rule

1 find the probability that the first event occurs
2. find the probability that the second occurs given that the first event occured
3 multiply these two probabilities

At least one rule

complement of at least one is none

mutually exclusive

two events A and B, A and B cannot occur at the same time, A and B have no outcomes in commmon

addition rule (or)

Probability of A or B, probability that event A or B will occur, P(A or B)
P(A or B)=
P(A)+P(B)-P(A and B)
if mutually exclusive ( P(A or B)= P(A)+P(B))