Monty Hall Problem
From "the Curious Incident Of The Dog In The Night Time" by Mark Haddon
Monty Hall Problem
You are on a game show on television. On this game show the idea is to win a car as a prize. The game show host shows you three doors. he says that there is a car behind one of the doors and there are goats behind the other two doors. he asks you to pick a door. you pick a door but the door is not opened. then the game show host opens one of the doors you did not pick to show a goat (because he knows what is behind the doors.). Then he says that you have one final chance to change your mind before the doors are opened and you get a car or a goat. so he ask you if you want to change your mind and pick the other unopened door instead. what should you do?
by intuition, i guess i won't not change my choice since there is a 50-50 chance between the two doors. but according to the answers, you shld change since there's a 2/3 chances that the other door is the one with the car.
The host now opens door 1. Since the host must always open a door revealing a goat, opening this door does not affect the chance that the car is behind the originally chosen door which remains 1/3. The car is not behind door 1, so the entire 2/3 probability of the two unchosen doors is now carried only by door 2, as shown below. Another way to state this is that if the car is behind either door 1 or 2, by opening door 1 the host has revealed it must be behind door 2.
so if you change, two out of three you get a car. and if you stick, you only get one out of two chances to win.
but it's really weird. why wouldn't the probability shift to only two doors after the door is opened? after all, only two doors are left. the reason stated was that the probability does not change as it doesn't depend on the past events coz there's this thing bout the host noeing the content of each door. so complicating. i'm getting a headache thinking.
http://en.wikipedia.org/wiki/Monty_Hall_problem has a very long and very complicating explaination. which i got lost after reading it. this problem really picked on my brain. very cool. imagine if this kinda problem comes up in some maths S paper qn. and this is at least one problem that maths has something to do with life. not like integration and binomial. i mean ppl, do use them in their lives. but only for ppl like physicist - they wanna calculate some funny formula on the fastest way to school etc. to win a nobel prize. Or teachers - they just need to do integration to teach and earn their keeps (haha! oops.) the rest of us just nv touch it eva again after we leave sch. pretty sad.
