The Monty Hall “problem”

I stumbled by chance on this book The Monty Hall Problem: The Remarkable Story of Math’s Most Contentious Brain Teaser on Amazon, or rather and more accurately Amazon suggested the book as connected to Burdzy’s The Search for Certainty. I first thought why would anyone need a whole book for explaining a simple conditioning argument (and the fallacy of conditioning on the wrong event) that I usually give as a problem to my second year undergraduates. But then I started reading the comments and found one that could not believe there was such a book because the answer was clearly 50-50! (Obviously, this comment was written by someone who had not read the book…) And I thus vaguely remembered a story about a highly respectable and respected statistician getting trapped by this puzzle… So maybe a book is in order. Maybe. But I find the argument of one of the commenters of the above disbelieving comment quite convincing: imagine there are 10,000 doors (instead of just 3), you pick one, the host opens 9,998 out of the 9,999 remaining ones and let you decide between switching  to the last remaining door and sticking to your original choice. Would you ever stick?!

5 Responses to “The Monty Hall “problem””

  1. […] are covered and justified (incl. the Wishart distribution). Paradoxes like Simpson’s, Monty Hall‘s, the Gambler’s Ruin, Allais‘, the Prisoner dilemma, are processed in specific […]

  2. […] The colloquium held today at Glasgow University in honour of Mike Titterington for his retiral was highly enjoyable! First, it was a pleasure to celebrate Mike’s achievements at this (early) stage of his career, along with people from Glasgow but also from all over the UK and even from Australia, among whom a lot of friends. Second, the (other) talks were highly interesting, with Peter Hall talking about the asymptotics of records, Byron Morgan about identifiability in capture-recapture models, Peter Green presenting a graphical diagnostic for spotting divergence between prior and likelihood in multivariate models, and Adrian Bowman illustrating advanced face analysis using principal curves on lips and faces. Third, I got a fair amount of questions and comments about ABC in general and ABC model choice in particular, including David Cox commenting that ABC was an important new topic and suggesting using goodness-of-fit tools for model comparison. The symposium per se ended up with a special cake covering some of Mike’s academic endeavours during the past years. While a formal affair, the diner was equally enjoyable, including a simultaneously witty and deep after-dinner talk paying tribute to Mike’s contributions by David Cox (who was Mike’s predecessor as editor of Biometrika) and a funny conclusion by John McColl who dug out a 1976 probability assignment he had from Mike that was the Monty Hall problem. […]

  3. […] Gill posted a paper on arXiv this morning about the Monty Hall problem. He does not mean to try yet another solution to the problem more susceptible to convince the army […]

  4. A lot of statisticians (or mathematicians) got it wrong and proudly wrote into a magazine with their reasoning!:

    • Thanks for the link, I knew about the strong reaction this toy problem created even in math circles and it is nice to have illustrations of such a range of disbelief, mostly due to conditioning on the wrong event. Each year I teach probability, this is the problem that creates the most debate in my class! Surprisingly, younger kids (like mine) have much less trouble getting the point.

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