probhw63.htm

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Additive rules To illustrate the additive rules, we shall consider the probability space with probabilities of outcomes as in the table below: outcome: | r | s | t | u | ---------------------------------------------- probability:| .1 | .4 | .2 | .3 | Let A={r, s}; B={s, t}; C={u} Additive rule for outcomes Additve rule for disjoint (mutually exclusive) events General additive rule Rules for complements Additive rule for outcomes The probability of an event is the sum of the probabilities in the outcomes in the event: P(A)=.1+.4=.5 P(B)=.4+.2=.6 P(C)=.3 P(AUB)=.1+.4+.2=.7, since AUB={r, s, t} P(AB)=.4, since AB={s} P(B')=.4, since B'={r, u} Additive rule for disjoint (mutually exclusive) events Two events X and Y are called disjoint or mutually exclusive if XY=Ø ({}, the empty or null set), i.e., X and Y do not share any outcome. P(XUY)=P(X)+P(Y) if X and Y are disjoint events. (The proof of this is just the associative rule of
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