For the following joint distribution of $X$ and $Y$, find the marginal probability $Pr(Y=2)$ , if $X$ and $Y$ are mutually independent. In the table below, blanks represent unknown probabilities that have to be determined should the value be required in the calculations.
I suspect I might have to solve some complicated linear system of equations, but I hope to find easier solutions.
Guide:
We know the value of $P(X=1, Y=3)$ and $P(X=2, Y=3)$.
From there, you should be able to deduce the value of $P(X=2,Y=2)$ since we know $P(X=1, Y=2)$.