Addition rule or not

CFA Level I Quant
#1

Hi Analysts

“The probability of X = 30% and Y = 40%. Calculate the probability that either will occur”.

When I saw this question, it seemed to me that I was missing the P(X|Y) or P(Y|X) so that I could calculate the P(XY) as P(XY) = P(X|Y) x P(Y).

How come the solution just says that P(XY) = P(X) x P(Y)? Is the conditional probability not necessary?

Kaplan says the solution is P(XY) = P(X) + P(Y) - (PXY).

All the best.

#2

read the problem again. My guess is that somewhere it says X and Y are independent.

#3

Does it say that X & Y are independent?

If not, then there’s not enough information to calculate the answer.

#4

Yes, it says that X & Y are independent. When that is the case, is it then possible to compute P(XY) just by multiplying the two?

#5

Yes.

#6

Just remember that when X and Y are independent, P(X|Y) = P(X).