Two numbers landing in different random groups

The numbers $1,2,\dots,100$ are randomly split into one group of $30$ and one group of $70$, with every such split equally likely. What is the probability that $6$ and $66$ end up in different groups?

$14/33$. Place $6$ first: it is in the small group with probability $\tfrac{30}{100}$, and then $66$ must be among the $70$ of the other $99$ slots in the large group; symmetrically for the other case. So $\tfrac{30}{100}\cdot\tfrac{70}{99}+\tfrac{70}{100}\cdot\tfrac{30}{99}=\tfrac{14}{33}$.