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Title / Subject - or probabilities are hard
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<blockquote data-quote="clearstream" data-source="post: 7270950" data-attributes="member: 71699"><p>Oops! Thanks, I did.</p><p></p><p></p><p>That's what I thought. What I found interesting is that obeying uniform random choice seems to overwrite the known odds. That seems identical to the naive error frequently made when first assessing the Monty Hall dilemma (to guess that odds are equal between the chosen door and the remaining door).</p><p></p><p>I'm familiar with the Monty Hall game, that's why I suggested it in this thread as a possible route for @<em><strong><u><a href="http://www.enworld.org/forum/member.php?u=12731" target="_blank">CapnZapp</a></u></strong></em> to take. Using the original framing (because it is clearer) we can make a very simple statement like</p><p></p><ol> <li data-xf-list-type="ol"> There are 3 doors, one hides a prize</li> <li data-xf-list-type="ol"> We get to pick one door</li> <li data-xf-list-type="ol"> Given we had no other information, the door we picked has a 1:3 chance to have the prize</li> <li data-xf-list-type="ol"> There is a 2:3 chance that the prize is behind one of the other doors</li> <li data-xf-list-type="ol"> One of those other doors, that is <em>certainly empty</em>, is revealed: that doesn't change the probability distributed among them so the last door has a 2:3 of being correct</li> </ol><p>Say the contestant says "<em>Hold on a minute here Monty, your conundrum is far too clever for me! I'll just flip this here nickel that I have in my pocket</em>." It should be clear to all observers that the chance of that nickel picking the door that has the prize is 50/50.</p><p></p><p>That was intended to be ironic. And funny. Ironically funny.</p><p></p><p>I'll get my coat...</p></blockquote><p></p>
[QUOTE="clearstream, post: 7270950, member: 71699"] Oops! Thanks, I did. That's what I thought. What I found interesting is that obeying uniform random choice seems to overwrite the known odds. That seems identical to the naive error frequently made when first assessing the Monty Hall dilemma (to guess that odds are equal between the chosen door and the remaining door). I'm familiar with the Monty Hall game, that's why I suggested it in this thread as a possible route for @[I][B][U][URL="http://www.enworld.org/forum/member.php?u=12731"]CapnZapp[/URL][/U][/B][/I] to take. Using the original framing (because it is clearer) we can make a very simple statement like [LIST=1] [*] There are 3 doors, one hides a prize [*] We get to pick one door [*] Given we had no other information, the door we picked has a 1:3 chance to have the prize [*] There is a 2:3 chance that the prize is behind one of the other doors [*] One of those other doors, that is [I]certainly empty[/I], is revealed: that doesn't change the probability distributed among them so the last door has a 2:3 of being correct [/LIST] Say the contestant says "[I]Hold on a minute here Monty, your conundrum is far too clever for me! I'll just flip this here nickel that I have in my pocket[/I]." It should be clear to all observers that the chance of that nickel picking the door that has the prize is 50/50. That was intended to be ironic. And funny. Ironically funny. I'll get my coat... [/QUOTE]
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