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I read the entire article. They all had defective reasoning. The player picked an option with a 1/3 chance of being right and a 2/3 chance of being wrong. The h
by ryao 2y ago
I read the entire article. They all had defective reasoning. The player picked an option with a 1/3 chance of being right and a 2/3 chance of being wrong. The host’s action did not change that. However, the host’s action did make the remaining door have a 2/3 chance of being right and a 1/3 chance of being wrong.
- Izkata 2y agoThis is downvoted, but correct. Which door is right and which door is wrong doesn't get reshuffled when the host removes a wrong door, so even though there's only 2 doors left the chance isn't 50:50, it's still 33:67 - with the player having most likely chosen a wrong door.
- alexey-salmin 2y agoIt's not correct. P(A|B)=P(A) only if A and B are independent. Requiring independence in this case literally means "the host opens the door regardless of the player making the right or wrong choice first time". It's a core assumption in your calculations, without it the math is not correct.