Should I Switch My Choice in the Monty Hall Problem?

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In summary, the conversation discusses the classic Monty Hall problem in which the probability of winning a car changes when one of the doors is opened. Despite the confusion, the probability of door 2 remains at 2/3, even after door 3 is revealed to have a goat behind it. This can be better understood by imagining 1000 doors, with 998 of them being opened to reveal empty spaces. In this scenario, it is clear that switching your choice would increase your chances of winning.
  • #1
chhitiz
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in 21, when kevin spacey plays 'the 3 doors' with the lead character in a classroom, the guy says something like:"before you opened the door, the probability of each door having a car was 33.33% but now since door 3 has a goat and i have door1, the probability of door 2 adds up to 66.66% so i will take door 2 now." shouldn't the probability have become 50% for both doors?
 
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  • #2
No! When door 1 was chosen, it had a probability of 1/3. Opening door 3 doesn't change that. Therefore door 2 has a probability of 2/3.
 
  • #3
It sounds like you're referring to the classic Monty Hall problem. The answer is indeed 2/3 but it assumes that you know the host's behavior exactly.
 
  • #4
Actually, door (2 or 3) had 2/3 probability. Now that door 3 has 0 prob after openning, prob of door 2 becomes 2/3.
To remove your confusion, think of 1000 doors behind one which there is a prize. You select one door and then 998 of the remaining doors are openned which are empty. Should you not then switch your choice?
 

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