## Probability Definition:

The likelihood of something happening or being the case.
Examples include probability of flipping a head, rolling a 6 on a single cube, or being born on a Sunday.

## Probability Terms to Know:

Experiment: a repeatable process with a set of possible results
Outcome: A possible result of an experiment
Sample Space: all the possible outcomes of an experiment
Event: one or more outcomes of an experiment

## General Probability Formula

 Probability of an event happening  = Number of ways the event can happen Total Number of Outcomes

## How To Write Probabilities:

Probability values can be written as a decimal, fraction, or percentage.

## Flip 1 Coin Example

A coin has 2 sides. 1 head, and 1 tail. So we have:
 Probability of Heads  = Total number of heads Total number of coin faces

 Probability of Heads  = 1 2

This can also be written as 50% or 0.5

## Roll Dice (Cube) Example:

A die/cube has 6 sides (1, 2, 3, 4, 5, 6) so we have:
 Probability of 3  = Total number of 3's Total number of die/cube faces

 Probability of 3  = 1 6

This can also be written as 16.67% or 0.1667

## Equally likely events:

For equally likely events, like coin flips and die rolls for instance, the probabilty for each event is 1/N where N is the number of possible outcomes

## Fruit in a Bowl Example:

Suppose we have a bowl of fruit with 3 apples, 5 oranges, and 6 bananas
We want to find out the probability of picking an orange

 Probability of picking an Orange  = Total oranges Total fruits

 Probability of picking an Orange  = 5 oranges 3 apples + 5 oranges + 6 bananas

 Probability of picking an Orange  = 5 14

This can also be written as 35.71% or 0.3571

## Probability Event Postulate:

For an Event A, 0 ≤ P(A) ≤ 1
A probability of 0 means the event is impossible.
A probability of 1 means the event is certain.
A probability of 0.5 or 1/2 or 50% means the event is equally likely to happen as it is not happen.
A probability greater than 1/2 or 0.5 or 50% and less than 1 is likely to happen.
A probability less than 1/2 or 0.5 or 50% and greater than 0 is unlikely to happen.

## Sample Space Postulate:

Sample Space: the set of all possible outcomes or results of that experiment.
For a Sample Space S (all possible outcomes), P(S) = 1 (since it is all possible outcomes)

## Empty Set Postulate:

Empty Set: The set with no elements
Probability of the empty set (event without outcomes) is: P(∅) = 0

## Complement of an event:

Complement of an event: The opposite of an event happening
AC
EventComplement
WinLose
RainNo Rain
Flip heads on a coinFlip tails on a coin

## Probability of the complement:

Given an Event A, the complement, A', is anything in the sample space which is not A
P(A') = 1 - P(A)

## Proof of the Probaility of the complement:

P(S) = 1 By the sample space postulate above
P(A U A') = 1
P(A) + P(A') = 1
P(A') = 1 - P(A)

##### How does the Probability Calculator work?
Free Probability Calculator - This lesson walks you through the basics of probability like the probability definition, events, outcomes, experiments, and probability postulates

### What 5 formulas are used for the Probability Calculator?

Probability of an event happening = Number of ways the event can happen/Total Number of Outcomes
For an Event A, 0 ≤ P(A) ≤ 1
P(S) = 1
P(∅) = 0
P(A') = 1 - P(A)

For more math formulas, check out our Formula Dossier

### What 10 concepts are covered in the Probability Calculator?

complement
The opposite of an event happening
AC
empty set
The set with no elements
event
a set of outcomes of an experiment to which a probability is assigned.
experiment
In statistics, a controlled and repeatable process
likelihood
how likely a particular population is to produce an observed sample
outcome
a possible result of an experiment or trial
postulate
A statement accepted as true without proof
probability
the likelihood of an event happening. This value is always between 0 and 1.
P(Event Happening) = Number of Ways the Even Can Happen / Total Number of Outcomes
sample space
the set of all possible outcomes or results of that experiment.
statistics
Statistics is a discipline concerned with the analysis of data and decision making based upon data.