Counting and Probability

Vocabulary

combination

selection of objects in groups where order does not matter

complement of an event

all outcomes in the sample space that are not the event

dependent events

events in an experiment in which the result of one event affects the probabilities of another event

event

subset of the outcomes in the sample space of an experiment

experiment

activity involving chance in which the outcomes are used to estimate probability

experimental probability

estimate of the likelihood of an event that is based on observations in an experiment

factorial

product of all natural numbers less than or equal to the indicated natural number. The factorial of zero is defined as one.

independent events

events in an experiment in which the result of one event does not affect the probability of another event

multiplication principle

for a process involving two steps, if there are mm ways to do step 1 and nn ways to do step 2, then there are m×nm\times n ways to complete the process. When there are more than two steps, multiply the number of ways each step can be done.

mutually exclusive events

events in an experiment that cannot occur at the same time

mutually inclusive events

events in an experiment that may occur at the same time

outcome

possible result of an experiment

permutation

selection and arrangement of objects in a certain order

probability

likelihood that an event will happen

probability model

list of all possible outcomes of an experiment with their corresponding probabilities

sample space

set of all possible outcomes in an experiment

set

collection of objects

theoretical probability

likelihood of an event that is determined by using a model

tree diagram

diagram that displays the sample space of an experiment so that the possible outcomes can be determined and counted