Let's test our Probability Skill: Monty Hall problem

arenaci

arenaci

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This problem is from the movie "21". What is your answer?

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?
 
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Mahdi

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yes, it is
simple probability question
before you had 33% chance that chosen door was right, now it`s 50% for second door to be with the car, so choice is here door 2 then
 
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ArcticWolf

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Yea it is to your advantage, 33% -> 50% I remember it was something like a moving window of probability.

Don't see much relation to poker probabilities though.
 
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619Leafs

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I have heard about this situation. You pick door 2. Better percentage of getting car.
 
arenaci

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You guys will be shocked by the correct answer. Guaranteed!
 
NWPatriot

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I have seen this before, but didn't buy it then either.

Yes, we have a 50% chance of being right if we change our selection, but we also have a 50% chance of being right by sticking with the original answer. This is because this is a new decision that has no dependence on the first decision. We were not required to predict a sequence of events, but are making two distinct decisions.

So where is the advantage?

The typical explanation is that because we had a 33% chance of being right when we made our first decision, then this is still our probability if we don't change. This is mathematics mumbo-jumbo. The math isn't wrong, it is just that the math is using the wrong constraints and assumptions. We we are making a second decision with a new set of constraints, so what difference does it make what our odds were before we make the second decision?
 
arenaci

arenaci

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NWPatriot said:
I have seen this before, but didn't buy it then either.

Yes, we have a 50% chance of being right if we change our selection, but we also have a 50% chance of being right by sticking with the original answer. This is because this is a new decision that has no dependence on the first decision. We were not required to predict a sequence of events, but are making two distinct decisions.

So where is the advantage?

The typical explanation is that because we had a 33% chance of being right when we made our first decision, then this is still our probability if we don't change. This is mathematics mumbo-jumbo. The math isn't wrong, it is just that the math is using the wrong constraints and assumptions. We we are making a second decision with a new set of constraints, so what difference does it make what our odds were before we make the second decision?
Click to expand...


Some say 33%. Some say 50%. But no one can guess the correct answer.
The correct answer is You change the door because when you change the door your probablity of winning is 2/3 (66%). I was shocked at first also. Lots of professors also rejected this but it was proven by simple math and simulations.:)
 
Vallet

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«Winner, winner, chicken dinner!»
Don't believe them. They saw the answer in the movie.:icon_rr:
 
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