Meta Rate My Team PokéBase - Pokémon Q&A
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Situation 1: Ditto and female Swinub with Oblivious
Situation 2: Ditto and female Swinub with Snow Cloak
Situation 3: Ditto and male Swinub with Oblivious
Situation 4: Ditto and male Swinub with Snow Cloak

What are the chances?

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In Generations III and IV, Abilities could not be inherited by breeding. An Egg would simply randomly be born with one of its possible Abilities.
Since Generation V, it has been possible for female Pokémon to pass down their Ability in some form when breeding with a male Pokémon. In Black and White, it was only possible for a female Pokémon to pass down its Ability if it had a Hidden Ability, at a 60% chance. Starting in Black 2 and White 2, this mechanic was updated so that females had an 80% chance of passing down their Ability slot, period. In Black 2 and White 2, this same 80% chance does not apply if a female Pokémon is bred with a Ditto, but starting in Pokémon X and Y, it does.
Before Generation VI, it was not possible for male or genderless Pokémon to pass down their Ability in any way. Starting in Generation VI, however, if these Pokémon have their Hidden Ability and are bred with Ditto, they have a 20% chance to pass it down to their offspring. Ditto's Ability is always irrelevant to inheritance.
If an Egg does not inherit its Ability from a parent, it can only be born with one of its non-Hidden Abilities.
- Bulbapedia

So, to answer your questions,

Situation 1: 80%.
Situation 2: 80%.
Situation 3: 50%, as male Pokémon can only pass down Hidden Abilities, so in this case, the male Pokemon's ability has no effect on the offspring's ability.
Situation 3: 50%, as male Pokémon can only pass down Hidden Abilities, so in this case, the male Pokemon's ability has no effect on the offspring's ability.


Hope I helped!

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