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
    12·
    2 days ago

    Really? The birthday problem is a super simple multiplication, you can do it on paper. The only thing you really need to understand is the inversion of probability (P(A) = 1 - P(not A)).

    The Monty hall problem… I’ve understood it at times, but every time I come back to it I have to figure it out again, usually with help. That shit is unintuitive.

    • naught101@lemmy.world
      1·
      10 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.

    • fine_sandy_bottom@discuss.tchncs.deEnglish
      1·
      12 hours ago

      My explanation is better:

      There’s three doors, of which one is the winner.

      First, pick a door to exclude. You have a 66% chance of correctly excluding a non-winning door.

      Next, Monty excludes a non- winning door with certainty.

      Finally, open the remaining door and take the prize!

    • Infernal_pizza@lemm.eeEnglish
      4·
      1 day ago

      My favourite explanation of the Monty hall problem is that you probably picked the wrong door as your first choice (because there’s 2/3 chance of it being wrong). Therefore once the third door is removed and you’re given the option to switch you should, because assuming you did pick the wrong door first then the other door has to be the right one