odds problem

We're on lets make a deal. We have door A, B, and C. We choose door A, and monty opens door B which is not the prize. Do we now have a 50% chance between A and C, OR do we have a 33.3% chance with A, and a 67% chance with C.

Mathmaticaly, it seems that the latter is true.

There is a 67% chance that B or C was correct, but now B has been revealed, leaving only C. It would therefore seem that A has a 33% chance of being correct, and C has a 67% chance of being correct, but every fiber of my being says that can't be right.

HELP!

Imagine a million doors.

You pick door #1. Monty now opens up doors #2 through #1,000,000 but keeps closed door #537,126.


He now asks you if you want to keep door number 1 or switch to 537,126. Now what should you do? 50-50 chance, right? Or is it 1 in a million chance that you picked right to begin with and it was door number 537,126 all along.


Same concept.

I use to think of it this way:


If A was right, then Monty had two possibilitys B and C.


If C was right Monty has to choose B


Therefore Monty will more often choose B when

you have misguessed the first time.


Kim

> but every fiber of my being says that can't be right. HELP!


Then you better work on your intuition as your math is right on the spot. You should always choose door C.


cu


Ignatius

First: you are very right by your mathematical calculation, there is a chance of 66.667% that door C is the right one...


I'm gonna explain it like this:

The only way for door C to be the wrong door is that you DID choose the right door from the beginning (33% chance of that).

So you change the odds from "against you" to "for you"

ahh, the old "ask marilyn" question rears its ugly head. for those that never saw it in print, she published it with the correct answer. later, she published all the letters she received from mathematicians/statisticians who were certain she had screwed up. she then proceeded to explain and prove her answer, along with a proposed experiment for classrooms across the country. as always, marilyn was right.

huge point in this is that monty KNOWS which door is the good door and will ALWAYS show you the bad door.

yes, always switch.

i first heard of this problem in my stat class in college. killed me till i figured it out.