201872215 71 Kok

I

.Experiments ,Models and Probabilities

1. I.Applying set theory to probability

(set algebra >Lprobability>

set event

element outcome

union

intersection

complement

universal set sample

sponge

5=41.2 . --.

. 6

*mutually exclusive f- disjoint):Ain Aj =§,itj

*collectively exhaustive :A,UAsu ...uAn =S

*Sample Space :finest grain ,mutually exclusive ,collectively exhaustive

set of all possible outcomes

1. 2.Probability Axioms

①PEAT Zo ,②PCS )=I

,

③PLA ,uAsu ...]=PLAN tPLAIT :

F

F

mutually exclusive events

1. 3.Conditional Probability

NAIB )=

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PCB)

1. 4.partitions and the law of Total Probability

*"A,partition IBi ,Bz ,

--.

.Bm 's ⇒PCA )=¥,

Plan Bi )

*Law of total probability :for apartition IBi ,Be

,

.

iii. Bm )

PLA)=

,

PCAIBIIPCB'D