probability
A number between 0 and 1 that describes the proportion of times an outcome of a chance process would occur in a very large number of repetitions.
law of large numbers
If we observe more and more repetitions of any chance process, the proportion of times that a specific outcome occurs approaches its probability.
simulation
Imitation of a chance process in a way that accurately models real-world outcomes.
probability model
Description of some chance process that consists of two parts: a list of all possible outcomes and a probability for each outcome.
sample space
List of all possible outcomes of a chance process.
event
Any collection of outcomes from some chance process. Events are usually designated by capital letters, like A, B, C, and so on.
complement rule
The probability that an event does not occur is 1 minus the probability that the event does occur. In symbols, P(AC) = 1 - P(A).
complement
The complement of event A, written as AC, is the event that A does not occur.
mutually exclusive
Two events A and B that have no outcomes in common and so can never occur together. That is, P(A and B) = 0.
addition rule for mutually exclusive events
If A and B are mutually exclusive events, P(A or B) = P(A) + P(B).
general addition rule
If A and B are two events resulting from some chance process, then the probability that event A or event B (or both) occur is P(A or B) = P(A) + P(B) ? P(A and B)
Venn diagram
A diagram that consists of one or more circles surrounded by a rectangle. Each circle represents an event. The region inside the rectangle represents the sample space of the chance process.
intersection
The event "A and B" is called the intersection of events A and B. It consists of all outcomes that are common to both events, as is denoted by A ? B.
union
The event "A or B" is called the union of events A and B. It consists of all outcomes in event A or event B, or both, and is denoted by A ? B.
conditional probability
Probability that one event happens given that another event is already known to have happened. The probability that event A happens given that event B has happened is denoted by P(A | B).
independent events
Two events are independent if knowing whether or not one event has occurred does not change the probability that the other event will happen. In other words, events A and B are independent if P(A | B) = P(A | BC) = P(A). Alternatively, events A and B are
general multiplication rule
For any chance process, the probability that events A and B both occur can be found using the formula P(A and B) = P(A) � P(B | A)
tree diagram
A diagram that shows the sample space of a chance process involving multiple stages. The probability of each outcome is shown on the corresponding branch of the tree. All probabilities after the first stage are conditional probabilities.
multiplication rule for independent events
If A and B are independent events, then the probability that A and B both occur is P(A and B) = P(A) � P(B)
multiplication counting principle
The result of a process involving multiple (r) steps; suppose that there are n1 ways to do Step 1, n2 ways to do Step 2, . . . , and nr ways to do Step r. The total number of different ways to complete the process is n1 � n2 �...� nr.
permutation
A distinct arrangement of some group of individuals where order matters.
factorial
For any positive integer n, its factorial n! is n! = n(n ? 1)(n ? 2) �...�3�2�1 In addition, we define 0! = 1.
combination
A selection of individuals from some group in which the order of selection doesn't matter.
?C?
The notation ?C? represents the number of different combinations of r individuals chosen from the entire group of n individuals.