# Probability Rules and Axioms

**Probability** is a way to **quantify the uncertainty** that arises from conducting experiments using a random sample from the population of interest.
**Probability **of an event happening = (Number of ways it can happen) / (Total number of outcomes)

**Example: ***the chances of rolling a '3' with a die*
Number of ways it can happen: 1
Total number of outcomes: 6
So the Probability = 1/6

### Important terms

**Sample Space:** all the possible outcomes of an experiment
**Sample Point:** just one of the possible outcomes
**Event:** one **or more** outcomes of an experiment

Example: the chances of a "double" when rolling 2 dice.
**Sample Space:** Possible outcomes. **36** **sample points**
{1,1} {1,2} {1,3} {1,4} ... {6,3} {6,4} {6,5} {6,6}

**Event:** Looking for double. Event is made up of **6** **sample points.
**{1,1} {2,2} {3,3} {4,4} {5,5} and {6,6}**
**
Run 100 **Experiments**, and find how many **Events **you observe.

## Probability Rules

**Probability Rule One:** For any event A, 0 ≤ P(A) ≤ 1
**Probability Rule Two:** The sum of the probabilities of all possible outcomes is 1.
**Probability Rule Three:** P(not A) = 1 – P(A)
**Probability Rule Four:** If A and B are disjoint events, then P(A or B) = P(A) + P(B)

## Probability Axioms

**Axiom One:** The probability of an event is a non-negative real number that is greater than or equal to 0.
**Axiom Two:** The probability of the entire sample space is one(no events exist outside of the sample space)
**Axiom Three:** If two events A and B are **mutually exclusive**, then the probability of either A or B [i.e P(A U B)] = P(A) + P(B)

Link: - MathsIsFun: Probability - ThoughtCo: What are Probability Axioms? - Basic Probability Rules

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