I have this probability table (function of $(x,y)$)
$\begin{array}{|c|ccc|} \hline X \setminus Y & 1 & 2 & 3 \\\hline 1 & a & b & c \\ 2 & 0.08 & 0.07 & d \\ \hline \end{array}$
I have to find $a,b,c$ and $d$. I know that $X$, $Y$ are independent and that $P(X=2|Y=1)=0.3$.
Well, I found $d$ relatively easily... Since they are independent I found that $P(X=2) = 0.3$, therefore $d=0.15$.
But could anyone help me find $a, b$ and $c$? I am trying somehow to reclaim this expression $p(x,y) = p(x)\cdot p(y)$ but I can't. Actually I only need to find $a$ and $b$, I can get $c$ easily since the sum of the table is $1$. But how?