17,259 words (≈ about 1 hour)
“A Cultural Paradox: Fun in Mathematics” is ideal for students who need a little push to get motivated, and also great for scientists and those in the math community that like to be in-the-know on relevant and current topics. Perfect as an accompaniment to any science class/course, this slim e-book can be read in the same time it takes to sit through one or two math classes, or roughly 68 minutes and 47 seconds.
Language: English
Written in: 2010
Published: 2010-07-08
Word count: 17,259 words (≈ about 1 hour)
License: Attribution Non-Commercial No Derivatives (cc by-nc-nd)
Tags: mathematics, culture, science, education
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Wed, 01 Sep 2010 12:36:47 +0200
Prochroma,
The mathematics is correct. The key is to realize that the second round (after Monty opened Door Two) probability for each of the remaining two doors should not be treated equally. This is what makes it such a counter intuitive problem. The typical response is that there is a mistake and insist that the doors have equal weight. For a more detailed explanation please refer to http://mathforum.org/dr/math/faq/faq.monty.hall.html.
Cheers,
Jeff
Wed, 01 Sep 2010 07:07:59 +0200
Jeffrey, I got to the end of 'pick a winner' fearing that the storytelling won over the discipline. After the door was opened you were prepared to reassign probability to door 3, but not to door 2. Both doors should have been treated equally. First round probability for each of three doors is 1/3. Second round probability for each of two doors is 1/2. To choose to switch vs not to switch, is a new choice, independent of the first round. Opening one more door would naturally produce certainty… (more)
Jeffrey, I got to the end of 'pick a winner' fearing that the storytelling won over the discipline. After the door was opened you were prepared to reassign probability to door 3, but not to door 2. Both doors should have been treated equally. First round probability for each of three doors is 1/3. Second round probability for each of two doors is 1/2. To choose to switch vs not to switch, is a new choice, independent of the first round. Opening one more door would naturally produce certainty as to the whereabouts of the prize, and the probability for the selected door becomes 0 or 1, not remaining at 1/3.
(less)Cheers, prochroma