Comments on: The Monty Hall Problem

By: Stubborn Mule

Stubborn Mule — Tue, 22 Jun 2010 01:07:54 +0000

OldFuzz: that argument is a perfectly reasonable explanation of Case 1. The main advantage of the approach I took is that, being more general, it allows you to handle a range of scenarios taking different approaches to what Monty knows and what he wants to do.

Danny: I certainly feel on more solid ground here because I’m really sticking to the “pure” mathematics, whereas with Tuesday’s child I was digging into the messier aspects of attempting to apply the mathematics to the “real” world (or as real as the hypothetical world of puzzles can be).

By: Danny Yee

Danny Yee — Mon, 21 Jun 2010 11:51:20 +0000

This seems pretty solid to me. You’ve teased out the different possible contexts of the problem nicely.

By: OldFuzz

OldFuzz — Mon, 21 Jun 2010 10:19:23 +0000

Stubborn

The touchy-feely, non-mathermatical solution to this problem (with a “knowing-all” Monty) is:

1. I choose a door, say No1
2. My probability of getting the car is clearly 1/3
3. Monty opens another and shows me a Goat . . . as he always can
4. Nothing I have done changes my probability of geting the car
5. Therefore my probability of getting the car is still 1/3 and the probability of the car being in the third door is now 2/3
6. Therefore I switch to get the 2/3 probability of the car.

This story was first put to me as a “pub quiz” on which many beers were won . .. and many brawls initiated by non-believers!