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
--Chuck
posted by Chuck at 1:51 PM
6 Comments:
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.
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.
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
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
i have a headache now.
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!!!!
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