Really, it is not that bad….
Music Somedays by Jack Anthony
Probability Powerpoint slides
Sampling Distributions Powerpoint slides
Hereis the diagram I made on the board in class:
[tags]Statistics, Probability, Sampling, Dave Brodbeck, Algoma University[/tags]
Cool–I get it! But…I still don’t get how, in the Monty Hall puzzle, the probability can change if a door is opened. The probability of having an ace doesn’t change if another card is turned over after the cards are dealt, does it?
(I liked Monty Hall’s answer: that’s not how the game was played. No one got to change doors. They got to choose something instead of the door.)
Ahh but those are fundamentally different problems.
The Monty Hall problem is usually listed like this: “suppose you’re on a game show, and you’re given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what’s behind the doors, opens another door, say No. 3, which has a goat. He then says to you, “Do you want to pick door No. 2?” Is it to your advantage to switch your choice’?
As the host knows what is behind each door, always opens a door revealing a goat, and always makes the offer to switch, opening a losing door does not change the probability of 1/3 that the car is behind the player’s initially chosen door. As there is only one other unopened door, the probability that this door conceals the car must be 2/3. It is therefore to the contestant’s advantage to switch to door 2.
(To avoid screwing this up, this is from a well written post on wikipedia). The thing most people miss is that the host knows where the car is, that changes everything.
I have to say it is a most nonintuitive (unintuitive?) answer, which is to say I understand what you said (much clearer than the explanation I was given in the past, thank you), but it doesn’t feel right. Which I suppose reinforces the point you made in class about how humans are really bad at intuiting probablities most of the time…