Wednesday, February 09, 2005

Probability Quiz

Well, I only got one response. For what it's worth, she was right. Statistically you should switch boxes. When you originally choose box 3 there is a 1 in 3 chance you are right. There is a 2 in 3 chance you are wrong. When I open a box I do not change the fundamentals of the problem. There is still a 1 in 3 chance of being right and 2 in 3 chance of being wrong. However now being wrong means that the $1000 is in box 2 (no other choice exists). So, you better switch. If you believe in statistics anyway.

--Chuck

6 Comments:

Blogger Binsky said...

This is the famous Lets Make a Deal Problem of should you switch doors after the host reveals one of them has nothing behind it.

2/09/2005 2:08 PM  
Blogger Clark said...

It does change the fundamentals of the problem, statistically. That's like saying if I flip a coin, there's a .00000000001% chance it could land on tails because originally the designers made coins have a trillion sides, but decided on only two right before you flipped the coin. How does it remain a one in three chance if it is definitely either in Box B or Box C now?

At first, there was a one in three chance because each box had an equal probability of containing the money: 33.67, 33.67, and 33.67 with a total of 100%. When you eliminate the first box from being a possibility, its chance drops to 0%, but the total must remain 100% so the remainder must be spread evenly to the remaining two boxes. This gives you 50% each, which is of course a 1 in 2 chance.

Plus I'd totally infer that you were trying to make me change my mind so I'd stick to my guns.

2/09/2005 2:41 PM  
Blogger Chuck said...

Binsky,
Congrat's, it is the famous Monty Hall problem. I just feel like it stumps most people as evidenced by Joe's comment.

Joe,
You are correct the probabilities do have to add up to 100%. However, you are still misled by the 50% 50% fallacy. Don't consider the boxes. Consider the options. Originally 1/3 in box 3 and 2/3 not in box three. Opening box 1 does not change that fundamental assumption. Now there is still 1/3 for box 3 and 2/3 for not box 3. Now, however, not box 3 means only box 2 because box 1 does not contain $1000. Therefore, box 2 has a 66.67% chance of having the money.

As Binsky pointed out this is only based on statistics not the social implications.

--Chuck

2/09/2005 2:48 PM  
Blogger Chuck said...

Joe,

I appologize if my previous comment sounded gruff. If you are interested in more resources follow the link below. This is a classical problem and although the solution I posted is anti-intuitive it is statistically correct.

http://www.cut-the-knot.org/hall.shtml

--Chuck

2/09/2005 3:11 PM  
Blogger Claire said...

i have a headache now.

2/09/2005 3:18 PM  
Blogger Andy said...

Haven't you seen let's make a deal?

"You chose door number 3! Let's see what you didn't win, open up door number 1! Its a car! You've seen something you didn't win, do you want to switch to door number 2?"

SWITCH!!!! USE YOUR FRIGGING BRAIN!!!!

2/09/2005 8:20 PM  

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