"Do they speak Chinese or English?"
Translation:Puhuvatko he kiinaa tai englantia?
When you use "tai", the answer could be "yes, both", "yes, Chinese", "yes, English" or "no". If you use "vai", it sounds like you know they speak either Chinese or English but don't know which one of the two it is. It might work if the sentence was "puhuvatko he italiaa vai espanjaa?" or something. However "vai" is also theoretically correct, I have added it as a possible translation.
Outilein answered this aready, but I like to add an example. When you ask something like: Do you by chance speak English or French? Then you use "tai", because the answer could be , is allowed to be,: " Yes,English ", "Yes, French", "Yes, both", "No, neither".
When you ask something like: " I know it must be either Finnish or Estonian... So, is it Finnish or Estonian? The answer can only be one of the two options.