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I'll throw in my explanation too: Your first choice is either right or it's wrong. If you switch, right becomes wrong and wrong becomes right. Your first choi
by patrickthebold 7y ago
I'll throw in my explanation too:
Your first choice is either right or it's wrong. If you switch, right becomes wrong and wrong becomes right.
Your first choice is 1/3 right 2/3 wrong.
- bhrgunatha 7y agoThe brilliance of the problem is that you're led to think that the odds have changed. I think there's a psychological component too. So many probability questions are about random events so you (very naturally) take a position that the revealed door is randomly chosen. It is NOT - you always see one of the goats.
- acomjean 7y ago> I think there's a psychological component too. You may be on to something. Perhaps part of it is not wanting to switch from a winning position to a losing one. Thats harder to take so inertia sets in.
- longerthoughts 7y ago>Perhaps part of it is not wanting to switch from a winning position to a losing one This is reminiscent of the endowment effect: https://en.wikipedia.org/wiki/Endowment_effect https://en.wikipedia.org/wiki/Endowment_effect
- WA 7y agoYeah exactly. The Monty Hall problem is about the probability of being correct with your first pick. It doesn’t really have anything to do with "changing probabilities".
- scooble 7y agoAh, that helps. I struggled with this because I didn't see the first choice as relevant to the final outcome. It is easy to see the game as restarted somehow when the 50/50 choice is presented.
- tnorthcutt 7y agoYep, same for me. Even though I understand (and believe!) the explanation of why switching is advantageous, a little voice still says "there's a 50% chance it's in one of the two remaining doors, because there are two doors and one prize!".