AS 2 Mathis Topic 5 Probability

A n B

Intersection of a and b

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A u B

In A and B and both
Both circles

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P(A u B) =

P(A u B) = P(A) + P(B) - P(A n B)
Can rearrange to get P(A n B) =

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Mutually Exclusive Events

Two outcomes that cannot occur at the same time are mutually exclusive. Eg choosing a black and red card from a deck of cards

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When A and B are mutually exclusive the intersection is

P(A n B) = 0
Therefore
P(A u B) = P(A) + P(B) - P(A n B)
P(A u B) = P(A) + P(B) - 0
So
P(A u B) = P(A) + P(B)

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Exhaustive Events
E.g. the event of selecting a black card from a deck and the event of selecting a red card from a deck of cards are exhaustive as all the cards are either black or red

If A and B are two events and they are cover all the possible outcomes then they are said to be exhaustive

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Therefore P(A u B) fro exhaustive events =

P(A u B) = 1

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Independent Events

When one event has no effect on another they are independent. Therefore, the probability of A happening is the same whether or not B has happened

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For Independent Events the P(A n B) =

P(A n B) = P(A) x P(B)

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Tree diagrams

multiply across branches
Add down branches

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Get Revising

AS 2 Mathis Topic 5 Probability

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Card 2

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Card 3

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Card 4

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Card 5

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