Comments on: Mind-Bending Probability Questions https://www.spencergreenberg.com/2017/09/1985/ Thu, 14 May 2026 20:54:37 +0000 hourly 1 https://wordpress.org/?v=7.0 By: Bullwinkle https://www.spencergreenberg.com/2017/09/1985/#comment-67797 Thu, 14 May 2026 20:54:37 +0000 https://www.spencergreenberg.com/?p=1985#comment-67797 Question 9: I don’t understand how switching your choice of the last two doors increases the chance of picking the gold goat. Also, How is that an opportunity to bet on Both doors? If 1,2,3, gives a 33% chance I pick 1, the host shows 3 and happens to be lead my chance of the two remaining should increase to 50%. But I only have the option to pick 1. Thats 50/50 I’ll pick the gold even if I switch choices. Right?

]]> By: Markus https://www.spencergreenberg.com/2017/09/1985/#comment-23434 Wed, 17 Mar 2021 18:38:52 +0000 https://www.spencergreenberg.com/?p=1985#comment-23434 Phew, mindbending indeed. Mindbending enough that I have to simulate them all to figure out the answer and still be mostly confused.

Question 2 sounds as if your explanation makes it arguably incorrect though, but I could be wrong and/or it’s just a bit too subjective: “conditioned on the fact that (i.e., assuming we are in a world where) all the die rolls ended up giving even numbers?” -> “in a world where” sounds like it’s just a rule in this world that dice end up showing even numbers. If this is the case however, we actually end up with an average of 3. It’s necessary for this question to result in the proposed 1.5 that the dice *can* show odd numbers, these are just not counted into the average.
I admittedly don’t get yet why that makes a difference though.

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