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The values of events A, B, and C are provided. Compare the probabilityof event A occurring, given that event C occurred to the probability ofEvent B happening, given that event C occurred (Compare P(A/C) toP(BIC)] Which event is more likely?P(A) = 0.45P(B) = 0.30P(C) = 0.25

User Wizzardz
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1 Answer

3 votes

The conditional probability P(A/C) is given by


P(A|C)=(P(A\cap C))/(P(C))

If event A is independent to event C, we can write


P(A|C)=(P(A)\cdot P(C))/(P(C))=P(A)

Similary, if event B is independent to event C, we get


P(B|C)=(P(B)\cdot P(C))/(P(C))=P(B)

Then, by comparing both results we can see that event A is more likey than event B.

User Kunchok Tashi
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