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

$P(A|C)=\frac{P(A\cap C)}{P(C)}$

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

$P(A|C)=\frac{P(A)\cdot P(C)}{P(C)}=P(A)$

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

$P(B|C)=\frac{P(B)\cdot P(C)}{P(C)}=P(B)$

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