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 resultsOutcome: 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 outcomesFruit in a Bowl Example:
Suppose we have a bowl of fruit with 3 apples, 5 oranges, and 6 bananasWe 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) ≤ 1A 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 happeningAC
Event | Complement |
---|---|
Win | Lose |
Rain | No Rain |
Flip heads on a coin | Flip tails on a coin |
Probability of the complement:
Given an Event A, the complement, A', is anything in the sample space which is not AP(A') = 1 - P(A)
Proof of the Probaility of the complement:
P(S) = 1 By the sample space postulate aboveP(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 OutcomesFor 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?
complementThe opposite of an event happeningACempty setThe set with no elements
∅eventa set of outcomes of an experiment to which a probability is assigned.experimentIn statistics, a controlled and repeatable processlikelihoodhow likely a particular population is to produce an observed sampleoutcomea possible result of an experiment or trialpostulateA statement accepted as true without proofprobabilitythe 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 Outcomessample space the set of all possible outcomes or results of that experiment.statisticsStatistics is a discipline concerned with the analysis of data and decision making based upon data.
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