Monday, April 21, 2008

if you guys had been an avid reader of xiaxue's blog,
the following topic im going to blog about would be very familiar to you. ;D
oh anyway, here it goes.

The Monty Hall Problem

the question is :

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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What's your answer?
I guess 100% of you said what's the point of switching? many people assume that each door has an equal probability and conclude that switching does not matter. That was my answer too !

As so, i continued reading and it says that:

in fact, in the usual interpretation of the problem the player should switch—doing so doubles the probability of winning the car from 1/3 to 2/3.

yea. mistified huh? go on reading. (:

Solution.
The chance of initially choosing the car is one in three, which is the overall chance of winning the car by sticking with this choice.
By contrast, the chance of initially choosing a door with a goat is two in three, and a player originally choosing a door with a goat wins by switching.
In both cases the host must reveal a goat. In the 2/3 case where the player initially chooses a goat, the host must reveal the other goat making the only remaining door the one with the car.


ok, i had this screenshot, but i just found out you cant zoom in. haha. or perhaps just visit the webby later :D

ok, put it in simple,
The player has an equal chance of initially selecting the car, Goat A, or Goat B. Switching results in a win 2/3 of the time because 2/3 of the time, the player's initial pick was a goat.
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Got the whole picture?
hmms. lets increase the number of doors to appreciate this better huh.

In this case there are 999,999 doors with goats behind them and one door with a prize. The player picks a door. The game host then opens all the doors with goats behind them, leaving two doors unopened. The host then offers the player the chance to switch to the only other unopened door. Do you switch?

YES you DO! By switching, your chances of winning increases tremendously from just a 0.001% to 99.99% !


dont believe? find out more here :D
it took me quite long before i digested this material. hahas [:
part of this post is credited to wikipedia.com and xiaxue.

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