geometry ch 13 vocab

probability

experiment

a situation involving chance (eg flipping a coin or rolling a die)

trial

a single performance of an experiment (eg rolling a die one time)

outcome

the result of a trial (eg landing on heads or tails)

• event: one or more outcomes or an experiment (the coin landing on tails)

the probability of an event…

is always between 0 and 1, inclusive (the sum of all probabilities of all possible outcomes must sum to 1)

theoretical probability

what should occur

experimental probability

what actually occurs when a probability experiment is repeated many times

sample space

the set of all possible outcomes (can be represented using an organized list, a table, or a tree diagram).

multi-stage experiments

experiments with more than two stages (experiments with two stages are called two-stage experiments)

the find the number of possible outcomes…

you can use the Fundamental Counting Principle: multiplying the number of possible outcomes from each stage or event

the factorial of a positive integer n

it is written n!, and is the product of the positive integers less than or equal to n

• n! = n times (n-1) times (n-2) times … times 2 times 1, where 0! = 1

permutations

the number of permutations of n distinct objects taken r at a time is denoted by nPr = n!/ (n-r)!

combination

an arrangement of objects in which order is not important. divide the number of permutations by the number of arrangements containing the same elements, r!

• nCr = n! / (n-r)!r!

geometric probability

probability that involves a geometric measure such as length or area

compound event

consists of two or more simple events. These can be independent or dependent.

independent events

if the probability that A occurs does not affect the probability that B occurs

• replacing an object

dependent events

the probability that A occurs in some way changes the probability that B occurs

• do not replace an object

the probability that two independent events both occur is the…

product of the probabilities of each individual event

• P(A and B) = P(A) times P(B)

the probability that two dependent events both occur is the…

product of the probability that the first even occurs and the probability that the second event occurs after the first event has already occurred

• P(A and B) = P(A) times P(B|A)

• P(B|A) is the conditional probability

an intersection of two sample spaces

P(A and B)

a union of two sample spaces

P(A or B)

mutually exclusive

if two events cannot happen at the same time (the two events have no outcomes in common)

• the probability that A or B occurs is the sum of the probabilities of each individual event

• P(A or B) = P(A) + P(B)

not mutually exclusive

if two events can happen at the same time (have outcomes in common)

• the probability that A or B occurs is the sum of their individual probabilities minus the probability that both A and B occur

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

• P(A and B) is the overlap

complement of an event A

consists of all the outcomes in the sample space that were not included as outcomes of event A

• P(not A) = 1 - P(A)