How to calculate probablities in a Bayesian network correctly?

Question

I want to solve this exercise and don't know how to calculate the probabilities below.

(a) I need to calculate the probability of Y if A and B are = 0 , am I correct?

I can write down the network as follows:

P(X,A,Y,B) = P(X) P(A|X) P(Y|X) P(B|Y)

Do I need to use variable elemination here? I just need a hint how to solve this.

Thanks!