# 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 $m$ ways to do step 1 and $n$ ways to do step 2, then there are $m\times n$ 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