## Probability

**Don't use percentages**use fractions or decimals

## Symbols

**P(?)**- Probability of

∪ - Or

**∩**- and

**A**- Variable

**A'**- not A

**P(A|B)**- Probability of A given B

**Mutually**- Events that can't occur at the same time.

__Exclusive__*Penny flipped twice*

**Conditional**- Events that occur because of the other or at the same time.

*Penny and Dice rolled same time*

## Probability Relationships

**Addition Rule**

Mutually Exclusive -

**P(A**

**∪**

**B) = P(A) + (B)**

Conditional -

**P(A**

**∪**

**B) = P(A) + P(B) - P(A**

**∩**

**B) - in formula booklet**

**Multiplication Rule**

Mutually Exclusive -

**P(A**

**∩**

**B) = P(A) x P(B)**

Conditional -

**P(A**

**∩**

**B) = P(A) x P(B|A) - in formula booklet**

When an event is

**mutually exclusive - P(A and B) = 0**

**Only the conditional rules are in the formula booklet**

## Venn Diagram

Venn diagrams plot probability values

Below is which values go where

Below is which values go where

If given values

The venn diagram will be

**P(A****∪****B) = 0.89, P(A****∩****B) = 0.33**and**P(A****∩****B) = 0.45**The venn diagram will be

## Tree Diagram

Going

Going

**across**branches -**multiply**Going

**down**branches -**addition****Conditional Variables**

This is when the first occurence occurs and then the second occurrence happens due to or because of the first occurrence

There is a

The

Bag of 10 counters, 3 blue and 7 red. One counter is chosen at random but not replaced. Another counter is chosen. Draw a labelled tree diagram to represent this data.

**E.g.**There is a

**bag of counters labelled A and B**. A counter is**chosen**and not**replaced**.**Another counter is chosen**.The

**second choice's probability**is**different**due to a counter being removed**Exam question:**Bag of 10 counters, 3 blue and 7 red. One counter is chosen at random but not replaced. Another counter is chosen. Draw a labelled tree diagram to represent this data.

**Mutually Exclusive / Independent Variables**

This is when the first and second occurrences

There is a bag of counters of A and B. A counter is chosen and

The

**happen independently**from each other**E.g.**There is a bag of counters of A and B. A counter is chosen and

**put back**. Another counter is chosen.The

**second choice's probability**is the**same****Exam Question:****Bag of 10 counters, 3 are red and 7 are blue. One counter is chosen at random and replaced. Another counter is chosen. Draw a labelled tree diagram to represent this**