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Monty Hall Puzzle

Question

Hi All,
I found this interesting puzzle called the Monty Hall Puzzle.
You are the contestant on a Game Show. There are 3 doors – say A,B and C – and behind one door is the prize of a million dollars. The prize is randomly placed and the probability of finding the prize behind any door is 1/3.
You get to pick one door and if you’ve picked the right door, you win the prize.
There’s a catch. After you’ve chosen a door, the game show host will not immediately open that particular door. The host will open another door that you did not pick and which he knows does not contain the prize. Suppose you had picked door A, and the prize is behind door B, the host will open door C and let you know that there is nothing being door C.
At this point, you will be given a choice: Do you want to stick with your original choice (door A in the example above) or do you want to choose the other unopened door (door B in this example)?
Do you think that switching doors would have any impact on the probability of finding the prize?
I thought that it would not make any difference (probability would remain at 50-50 for the two open doors)
Surprisingly, it turns out that you SHOULD switch.
Explaining the Monty Hall Puzzle
Let’s the divide the doors into two sets
Set 1: {The door you picked originally}
The Probability that the prize is in Set 1 is 1/3
Set 2: {The other two doors}
The Probability that the prize is in Set 2 is 2/3
The Host will open a door from Set 2 that does NOT have the prize, but the probability that the prize is in Set 2 still remains at 2/3.
Switching your choice to choose the remaining unopened door from Set 2 maximizes your odds of winning.

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Hi.

That's a standard puzzle and you gave what I think is the best short answer

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23 hours ago, CodeGroundOnlineTests said:

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You can use the Search feature here to see whether a puzzle might have been already posted.
Mouse over Activity tab and click on Search.

A version of Monty Hall has in fact been posted here, although with enough different terminology it's hard to find.
Either way, a member might know of a previous post and simply direct discussion to it.

Regarding usefulness, puzzles are usually posted without the solution.

This permits members to post their responses to your puzzle.
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Simply highlight the part of your post to be hidden and click on the eye icon and then submit your post.

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