# Probability

Description of probability

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## Rules of Probability

• Probability is always less than one, greater than 0﻿
• Sample space - All possible outcomes
• Event - Set of possible outcomes
• P(A n B) = Probability of A and B happening (intersection)
• P(A u B) = Probability of A or B happening (add the 2 values that are not the intersection)
• P(A|B) = Probability of A given that B happened (conditional probability)
• P(A') = Probability of A not happening
• P(A) + P(A') = 1
• Addition Rule - P(A u B) = P(A) + P(B) - P(A n B)
• Multiplication Rule - P(A n B) = P(A|B) x P(B) or P(B|A) x P(A)
• If A and B are independent, P(A n B) = P(A) x P(B)
• If A and B are mutually exclusive, P(A n B) = 0
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## Venn Diagrams and Tree Diagrams

A Venn diagram gives 4 peices of information -

• The "A" box gives the value of A n B'
• The "B" box gives the value of B n A'
• The intersection gives the value of A n B
• The outside of the circles gives the value of A' n B'

Tree diagrams -

Multiply along the branches, add down the branches

If A and B events are both independent, P(B|A) = P(B)

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