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.
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.
Cheers, prochroma
As a post-college member of society I've been on a mission to expand my horizons, more specifically a quest of giving second chances (particularly to things that once made me curse the heavens) thus my reading a book about math. A friend of mine suggested it and I can honestly say that no bias in the world could have made me like math...nope, either math won me over or my heart would remain stone. (I went to an arts college that did not require math classes...one of the reasons I picked it.)… (more)
As a post-college member of society I've been on a mission to expand my horizons, more specifically a quest of giving second chances (particularly to things that once made me curse the heavens) thus my reading a book about math. A friend of mine suggested it and I can honestly say that no bias in the world could have made me like math...nope, either math won me over or my heart would remain stone. (I went to an arts college that did not require math classes...one of the reasons I picked it.)
Friends, this book is such a great delight that I needed to share it. It's made me think about the Universe a little differently and although I may not go out and take a Trig class it certainly challenged my long held feelings on this mysterious thing called 'math.' The book is a quick read with short (but insightful) chapters and not a hint of confusing math lingo. Not once did I feel like I was being lectured at but rather a dialogue was being created between myself and the author. I felt that the author simply wanted to share his love and passion for a subject he sees being misunderstood all the time. I cannot recommend this book more...but I’ll try! It’s an amazing read and a great way to inspire those who thought they were done with math. Perhaps it will inspire someone to re-explore math but at the very least I believe it will lead to understanding and respecting math for the beautiful part of the Universe it is.
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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
Tue, 10 Aug 2010 18:43:44 +0200
As a post-college member of society I've been on a mission to expand my horizons, more specifically a quest of giving second chances (particularly to things that once made me curse the heavens) thus my reading a book about math. A friend of mine suggested it and I can honestly say that no bias in the world could have made me like math...nope, either math won me over or my heart would remain stone. (I went to an arts college that did not require math classes...one of the reasons I picked it.)… (more)
As a post-college member of society I've been on a mission to expand my horizons, more specifically a quest of giving second chances (particularly to things that once made me curse the heavens) thus my reading a book about math. A friend of mine suggested it and I can honestly say that no bias in the world could have made me like math...nope, either math won me over or my heart would remain stone. (I went to an arts college that did not require math classes...one of the reasons I picked it.)
Friends, this book is such a great delight that I needed to share it. It's made me think about the Universe a little differently and although I may not go out and take a Trig class it certainly challenged my long held feelings on this mysterious thing called 'math.' The book is a quick read with short (but insightful) chapters and not a hint of confusing math lingo. Not once did I feel like I was being lectured at but rather a dialogue was being created between myself and the author. I felt that the author simply wanted to share his love and passion for a subject he sees being misunderstood all the time. I cannot recommend this book more...but I’ll try! It’s an amazing read and a great way to inspire those who thought they were done with math. Perhaps it will inspire someone to re-explore math but at the very least I believe it will lead to understanding and respecting math for the beautiful part of the Universe it is.
(less)Fri, 16 Jul 2010 02:34:57 +0200
I appreciate getting your feedback, especially if you enjoyed something but more importantly I hope you enjoy the math! - Jeff