Correctness of Freivald algorithm for checking matrix multiplication, why is the probability of checking $AB \neq C$ at least 1/2?
Let $G$ be the number of good vectors, and $B$ be the number of bad vectors. The proof shows that $G \geq B$, since the mapping from the bad vectors to the good ones is one-to-one. Since all vectors are equally likely,
$$ \Pr[Dr \neq 0] = \frac{G}{G+B} \geq \frac{1}{2}. $$
The last inequality is a bit of algebra I leave to you.