Thursday, January 29, 2009

brainstorm >> 3

i was inspired to make this post by a post on kepalakotak
it had been on my mind since form 5...
but it wasn't till then that i really looked into it...


so, here's the situation (also known as the monty hall problem)

You're in a game show...
there are 3 doors...
behind one of them is a car...
behind the other 2, are goats...

the host let's you choose 1 door..
if you choose the right door
you win the car !
if you choose the wrong door
you don't win the car!
simple as that...

so, you chose a door....
and you're hearts racing whether you made the right choice or not !

before revealing if you made the right choice or not,
the host opens 1 of the remaining 2 doors...
behind it is a goat!

so only two doors remain, a goat and a car...

the host then gives you the option
of either staying with your chosen door,
or change to the other closed door...


The Question...

What should you do to maximize the probability of winning the prize? Should you stick with your first choice, or switch to the other door?
Or does it not matter?



18 comments:

anwar azhari said...

d thing is,

in any door we choose, d host wud open a door which wud lead 2 d goat, just to make us change our mind and be physic by d host action.

i dunt think tht theres any answer 2 ths q but i think tht ur trying 2 show us tht d host is playing a lil mind trick on us.

in other mean,
y wud d host increase our problity 2 get the car?

i mean, at 1st we wud make d corrct choice by 1/3, n next after he open 1 of d door d prob wud 1/2???

i think this is just a minute pyhsic action

Anonymous said...

so, the q is wut should we do to maximise our chance of winning..
n we only have 2 choices..eithr stick with the old door or choose the other door, rite?
klo cam2 x de beza la kn??coz either 1 pon still probabilitynye 1/2..

ke...

ade maksud tersirat in the sentence itself..?

aisyah said...

If to maximize the probability,I'll agree with anonymous..coz the probability is still 1/2...

but, if I've been asked wether to stick with my first choice,or choose the other door,I'll stick with my first choice,bcoz u said that if I choose the right door I'll get the car..hmmm..

Muhammad Anas bin Kamarudin said...

hmmm... we only have 2 choices...

STAYING or SWITCHING doors...

most people would come to say that it doesn't matter... it's a 50/50 situation... plain luck
just as you guys have come to...

now..

what if i were to say... that the chances/probability of winning in one of the choices is higher than the other?

which choice would that be and why?? or do you bluntly disagree? and say it's 50/50!

haa... cane?

ammar said...

change it. the percentage is 66%. put your emotions aside. (I watched 21 twice)

aisyah said...

I think I'll stick 2 my 1st choice...Through my psychological knowledge(hehe) the host has known that my 1st choice is right....So that, he opened one of the doors...just to make me confused and change my choice...huhu...

Is my reason can be accepted?

Muhammad Anas bin Kamarudin said...

huhu.. no comment...... yet... baru sgt post... nt spoil

anybody else?... come on... just write down what you think guys... x yah malu2... betul salah bukan yang penting... yg pnting pendapat anda... *peace*

amaraman said...

arh!arh!adoi!adoi!(menggaru badan yg tough) i'm itching to tell but i don't wanna spoil the fun for those who still don't know. like anas said "baru sgt post... nt spoil"

Muhammad Anas bin Kamarudin said...

i know ammar!! i'm itching in my pants right now to tell them!! hahaha

(menggaru badan yg tough)>>> xley belah dowh ayat ko... hahaha

Anonymous said...

switching!
nk kene btau ke npe?
nnt spoiler plak..(huhu bajet btol je)
tp ni agak jela..

Muhammad Anas bin Kamarudin said...

answers galore..

http://en.wikipedia.org/wiki/Monty_Hall_Problem

Muhammad Anas bin Kamarudin said...

Switching gives you a higher chance of winning...

the Rasional behind this....

is that you are more probable to choose a door with a goat (2/3) at the beginning compared to choosing a door with the car (1/3)...

so you choose a door
(2 out of 3 chance is a goat)
(1 out of 3 chance is the car)

the host then opens one of the 2 remaining doors, revealing a goat... only 2 doors left...

at a glance, it may seem like a 50/50 chance... but since the door you chose is most probably a goat... switching gives you a better chance of winning...




it may be easier to look at it if there were 10 doors... 1 car, 9 goats...

you choose a door
(9/10 chance being a goat)
(1/10 chance being the car)

the host then opens 8 doors, all containing goats, leaving your door and 1 other mysterious door..

hmmm.. to change, or not to change, that is the question...

of changing would give you a better chance, since its a 9/10 possibility that your door is a goat...

huhu... i didn't see it at 1st either... my friend asked me this Q and told me switching is better, but he didn't remember why... i kept saying it's 50/50!...

Anonymous said...

sori,but i don't agree..
aku pown pilih switching tp bkn atas sbb tu..

klo ikut percentage, after 1 door da remove,tinggal 2 doors je, btol?
cemane pon mestila 50/50.
probability 2/3 tu before host tu pilih 1 pintu..
but after that,it's a diff story

aku rse agak mush ma'ul klo nk samakn ngan cth 10 pintu tu..

math is about numbers..klo no tu sndr da berubah, caner result bley same?

Anonymous said...

pd pendapat aku..(open ea?perbincangan sihat..huhu)

aku pilih swicthing sebab based on maksud perkataan tu sendiri

verb (past and past participle switched, present participle switch·ing, 3rd person present singular switch·es)

Definition:

1. transitive and intransitive verb change, shift, or transfer: to change from one time, activity, or situation to another, often quickly or suddenly, or cause somebody or something to make such a change
The dancing class has been switched from Friday afternoon to Saturday morning.


2. transitive and intransitive verb make exchange or substitution: to exchange two similar or related things, or put one in the place of the other, sometimes secretly or surreptitiously


3. transitive and intransitive verb electricity change electrical function: to make an electrical device do something different by operating a switch to cause current to stop or start flowing or change its path
He switched the radio to a different station.


4. transitive and intransitive verb U.S. rail move train between tracks: to move a locomotive or train from one track to another


5. transitive and intransitive verb flick or swing to and fro: to move quickly from side to side or backward and forward, or make something move in this way
The cat switched her tail in annoyance.


6. transitive verb beat somebody with switch: to beat somebody with a switch, especially as a punishment

klo amek definition no 6, aku assume when kte beat the door, klo pintu tu ade kambing,mesti die mengembek or something la..
so probability nk dpt kete lg tinggi coz kete x leh ngembek,or make any other sounds on its own,for that matter..

diterima x? ke terlalu abstract thinking??kui3

Anonymous said...

btw,ni sumer org yg sme..

Muhammad Anas bin Kamarudin said...

dear anonymous...

thank you for your opinion(s)

regarding your former comment...
memang x dinafikan tinggal 2 pintu, but it's not 50/50...

lain la kalo kita x pilih lagi... then host bukak 1 pintu, reveals a goat.... then asks us to pick...

if that was the case, then our chances would be 50/50
kan?

BUT, that's not the case... we chose a door when there were 3... so the door we chose, would
2/3 be a goat
1/3 be a car

so....

after the host opens the 3rd door...

staying would result in ;
2/3 lose
1/3 win

switching would result in ;
2/3 win
1/3 lose

p/s: i changed it to 10 doors for it to be seen more clearly...

here's an analogy

i have to peices of rope
i want to identify the longer one

which 2 sets of ropes would be easier to do so

25cm and 25.1 cm ropes

~or~

25cm and 35 cm ropes?

let me ask you... in determining the longer piece of rope, does the magnitude of the rope being longer matter.

25.1cm and 35cm are both longer than 25cm... but which one is more obvious?? that's simply what i did...

ke ada hujah lain nak support pendapat anonymous?

Muhammad Anas bin Kamarudin said...

regarding the latter comment... i have no comment... huhu... but that was certainly unexpected...

Anonymous said...

'unexpected' is a comment pe...