if E(X) = 1.6 and E(Y) = 2
does E (Y/X) = E(Y)/E(X)
2/1.6 ??
That doesn't bode well.
What are the possible values of Y/X ......? 1/1 = 1, 1/2, 2/1 = 2, 2/2 = 1 (already considered), 3/1 = 3, 3/2.
Pr(Y/X = 1) = Pr(Y = 1 and X = 1) + Pr(Y = 2 and X = 2) = (0.3)(0.4) + (0.4)(0.6) = 0.12 + 0.24 = 0.36.
Pr(Y/X = 1/2) = Pr(Y = 1 and X = 2) = (0.3)(0.6) = 0.18.
etc.
Then E(Y/X) = (1)(0.36) + (1/2)(0.18) + ......
This is the same calculation as CaptainB did - all I've done is simplified the arithmetic.
They are random variables, not events. We are finding expectations, which are properties of RV.
Also no one has used P(Y/X) as a notation (which if they had might be mistaken for the conditional probability P(Y|X) but neither I nor MrF would do that -would we?)
Also , please quote what you are replying to so we know what you are talking about (and if you don't know what you are talking about don't talk about it).
CB