Question

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

Answer 1

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.