Monty Hall Paradox!

I was lying in bed last night, wondering how the Monty Hall paradox can be explained well, and figured it could only happen if i change my perception a bit.

What is the Monty Hall problem? well he is a game show host.. of the show called “Deal or No Deal” .. [the copy of it is made in indian TV as well.. i dnt remember the name of the game, but Aman Verma was the host as far as i remember] Anyway, back to the problem,

Consider three doors. Behind one is a car, and behind two others are goats. You are asked to choose one door – if it’s the one with the car, you win. otherwise, you lose.

you choose one car. Then Monty (the gameshow host) opens one of the other doors to show a goat behind it. You are given the chance to change your choice of door to the other closed one – should you?

The answer is Yes. the /intuitive/ answer is that there is a 50% chance either way, but mathematically, there is actually a 66% chance.

Took me a good few minutes to figure out how to verify it. I kept thinking of it as “there is a 33% chance of me picking the right one. door opens. I now have… 50%?”. Couldn’t seem to make the leap for some reason.

That was a result of wrong perception – you need to think of it from the point of view of what is /not/ the right door.

1. choose one door. the chance of the car being behind one of the other doors is 66%.
2. one of the other doors opens. the chance is still 66%!.
3. You now have two closed doors. the door you /did not originally choose/ has a higher chance than the one you did choose, so you should switch.

well.. wikipedia explains it much better than me.. so here is the link..
http://en.wikipedia.org/wiki/Monty_Hall_problem.

The interesting fact is, it actually makes me question the perception norms.
does it to you?

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