Probability

is used when each outcome in a sample space is equally likely to occur.P(E)= number of outcomes in event E total # of outcomes in sample space

is based on observations obtained from probability experiments.P(E)= Frequency of event E = f Total frequency h

the set of all outcomes in a sample space that are not included in event E.

Keyword "OR"

Mutually Exclusive Events are events that cannot occur at the same time.If A and B are mutually exclusive,P(A and B) = 0If A and B are mutually exclusive, P(A or B) = P(A) + P(B)

If A and B are not mutually exclusive then, P(A or B) = P(A) + P(B) - P(A and B)

an action, or trail, through which specific results (counts, measurements, or responses) are obtained.

the results of a single trail in a probability experiment.

the set of all possible outcomes of a probability experiment.

a subset of the dample space. May consist of one or more outcomes.

an event that consists of a single outcome.

Keyword "AND"

if the occurence of 1 event does not affect the probability of the other evert. Two events A &B are independent if P(B/A)= P(B) or if P(A/B)=P(A)

events that are not independent are dependent.

the probability of an event occurring, given that another event has already occurred. The conditional probability of event B occurring, given that event A has occurred, is denoted by P(B/A).

results from intution, educated guesses, and estimates.

as an experiment is repeated over and over, the emperical probability of an event approaches the theoretical (actual) probability.

if 1 event can occur in m ways and a second event can occur n ways. The # of ways the two events can occur in sequence is m*n. This rule can be extended for any # of events occurring in sequence.

A password consists of two letters followed by a five-digit number. How many passwords are possible if (a) there are no restrictions and (b) none of the letters or digits can be repeated?(a) 26*26*10*10*10*10*10= 67,600,000(b) 26*25*10*9*8*7*6= 19,656,000

an ordered arrangement of objects. The # of different permutations of n distinct objects is n!

Eight people compete in a downhill ski race. Assuming that there are no ties, in how many different orders can the skiers finish.=40,320

a selection of r objects from a group of n objects without regard to order and is denoted by nCr. The # of combinations of r objects selected from a group of n objects isnCr= n! (n-r)!r!

A lottery has 52 numbers. In how many different ways can 6 of the numbers be selected? (Assume that order of selection is not important.)=52 C 6=20,358,520

the probability of an event E is between 1 and 0, inclusive.