Friday math movie - NUMB3RS and Bayes’ Theorem
By Murray Bourne, 23 Nov 2007
There are 2 related videos for your viewing pleasure this week.
Here's Charlie (the main character in the NUMB3RS tv series) explaining the Monty Hall problem to his students. It has a good twist, of course. What you expect intuitively is not the best decision.
Here is another explanation of the same thing from Ron Clarke (which has a bit of a Monty Python feel):
Here's quite a good (if lengthy) explanation of Bayes' Theorem. From the page's intro:
... an excruciatingly gentle introduction.
There's a bunch of Java applets on that page that let you play with the concepts and investigate the meaning.
See the 5 Comments below.
27 Nov 2007 at 1:33 pm [Comment permalink]
Cool videos; I love the Monty Hall problem!
P.S. It should be “Bayes’ theorem”; it’s named after Thomas Bayes.
27 Nov 2007 at 9:46 pm [Comment permalink]
Doh - thanks, Darmok. Yes, I knew it was Bayes apostrophe - but after years of typing 'apostrophe s', it kinda becomes a habit.
I have corrected it in the post.
2 Dec 2007 at 5:10 am [Comment permalink]
Iam going to put a link to this information. I saw this Numb3ers episode last weeK and I enjoy. Thanks.
4 Feb 2010 at 4:10 am [Comment permalink]
that's interesting Charlie!
28 Dec 2016 at 10:15 pm [Comment permalink]
I disagree with the usage of Bayes Theorem to solve the Monty Hall problems.
If there are 3 choices, you pick 1 of the 3 (1/3 probability being the same as 2/6 probability), and the host removes 1 of the other 2 options (1/3 probability being the same as 2/6 probability), then, 1/2 (50%, being 1/6) from the choice removed by the host should be transferred to your selection, and the other 1/2 probability (likewise 50%, being 1/6) should be transferred to the other option that you may or may not switch to.
At that point the 2 remaining selections (yours, originally 2/6, now plus the 1/6 from the removed option, being 3/6, which is the same as 1/2 or 50%) is equal to the other option (originally 2/6, now plus the 1/6 from the removed option, being 3/6, which is also the same as 1/2 or 50%).
So, to me, you are now positioned at 50:50 (3/6 v. 3/6), and not 2/3 to 1/3. Consequently, you have an even probability of selecting a car/goat in the Monty Hall/NUMB3RS video example, and not a 2:1 probability as most of these videos state as fact.