Wikipedia defines common sense as “knowledge, judgement, and taste which is more or less universal and which is held more or less without reflection or argument”

Try to avoid using this topic to express niche or unpopular opinions (they’re a dime a dozen) but instead consider provable intuitive facts.

  • naught101@lemmy.world
    1·
    15 hours ago

    Adding my own explanation, because I think it clicks better for me (especially when I write it down):

    1. Pick a door. You have a 66% chance of picking a wrong door, and a 33% of picking the right door.
    2. Monty excludes a door with 100% certainty
    3. IF you picked a wrong door, then there’s a 100% chance the remaining door is correct (so the contingent probability is p(switch|picked wrong) = 100%), so the total chance of the remaining door being correct is p(switch|picked wrong)* p(picked wrong) = 66%.
    4. IF you picked the right door, then Monty’s reveal gives you no new information, because both the other doors were wrong, so p(switch|picked right) = 50%, which means that p(switch|picked right) * p(picked right) = 50% * 33% = 17%.
    5. p(don't switch|picked wrong) * p(picked wrong) = 50% * 66% = 33% (because of the remaining doors including the one you picked, you have no more information)
    6. p(don't switch|picked right) * p(picked right) = 50% * 33% = 17% (because both of the unpicked doors are wrong, Monty didn’t give you more information)

    So there’s a strong benefit of switching (66% to 33%) if you picked wrong, and even odds of switching if you picked right (17% in both cases).

    Please feel free to correct me if I’m wrong here.