Is it worth taking risk?
Me and my friend were on vacation in Las Vegas. We both have contradicting personalities. He is a risk taker while I am not. We were playing the Guessing Game in one of the casinos. The game is very simple. There are three boxes say A, B, C where only one of the boxes contains the prize. You need to play all three steps of the game before you claim the prize.
Step 1: You are supposed to guess the box containing the prize. Ofcourse all three boxes are equally probable. Say you chose box A.
Step 2: The game host will then open one of the other two boxes which does not have the prize. That is he wont open the box A as you have already chosen it in step 1. Hence, he will either open box B or C depending on which ever doesnt have the prize. Lets say he opened Box B.
Step 3: In this step, you can either claim the prize from the box A which you chose in first step or you can choose the other unopened box (Box C).
My friend claims, you will always increase your chances of winning if you choose a different box in step 3 rather than trusting your first instinct in step 1. But I argue it doesnt matter as both boxes have equal probability of containing the prize. Do you think taking the risk of switching the boxes increases your chances of winning?
NOTE: There are no tricks in the question. It is purely logical reasoning and the laws of probability.
[HINT: Try to think from the point of view of the game host rather than as a player.]
posted by Rajesh Munavalli @ 1:52 PM
5 comments
5 Comments:
No you are not missing anything. Just to put you in the right direction. It does matter if you switch or not.
HINT: Try to think from the point of view of the game host rather than as a player.
That is the correct answer Srikanth.
I beg to disagree. The question is whether your chances of winning increase. Even after one is exposed the probabilities remain the same for the remaining two 1/3 and 1/3. But truly at that moment it changes to 1/2 and 1/2. This is purely a logical thought, but probably am missing something.
Paul...what you are missing is the information contained in exposing one of the boxes. If you imagine yourself in the host's position, which one would you expose?. There are two situations...
Situation 1: The player has chosen the box with the prize. In that case you as a host would open any of the boxes. This is the case when the player will loose, if he picks the other box. There is 1/3 of chance this situation will happen.
Situation 2: The player has not chosen the box with the prize. In that case you as a host can open ONLY ONE box as the other has the prize. This is the case when the player will win, if he picks the other box. There is 2/3 of chances this sitaution will happen.
Does that clarify?
Gotchaa Rajesh. Didnt realize the host already knew the box containing the prize. You kept hinting at thinking from the hosts point of view - slow wednesday for me i guess .. :)
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