If I know $P(x)$ and $P(y|x)$, how can I know $P(y)$?

Question

If I need to compute $P(y)$ and I only know $P(y|x)$ and $P(x)$.

I know that:

$$P(y|x)=\frac{P(y,x)}{P(x)}$$

This is the contingency table for $P(y|x)$:

 P(y|x) |   +x   |  ¬x  |
-------------------------
   +y   |  0.91  | 0.03 |
-------------------------
   ¬y   |  0.09  | 0.97 |
-------------------------

And the probability of $x$:

        |   +x   |  ¬x  |
-------------------------
  P(x)  |  0.05  | 0.95 |
-------------------------

How can I compute $P(y)$?

Answer 1

$P(y,x) = P(y|x) P(x)$

$P(y) = \sum_x P(y,x) = \sum_x P(y|x) P(x) $