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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Other cards in this set
Card 2
Front
A u B
Back
In A and B and both
Both circles
Card 3
Front
P(A u B) =
Back
Card 4
Front
Mutually Exclusive Events
Back
Card 5
Front
When A and B are mutually exclusive the intersection is
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