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))