If I have a Pokemon with a Hidden Ability (let's say Whismur), and I breed it with another Pokemon (like Ditto), will the hatched Pokemon also have the same ability as its non-Ditto parent?
Yes it will, there is a chance that the Hidden Ability will be passed down to the egg.
If a female Pokémon has a Hidden Ability and is bred, it has a 60% chance of giving that Ability to each of its children. Each of the other Abilities has a 20% chance of being passed down. In Generation V, Hidden Abilities cannot be passed down from male or genderless Pokémon, or when breeding with Ditto. In Generation VI, this was changed so that male and genderless Pokémon have the chance to pass down their Hidden Ability only when bred with Ditto.
