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Offline Blue

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What are the odds...
« on: May 05, 2006, 02:59:33 PM »
If yuh dont like maths leave dis thread now!  ;D

I am a mathematician by trade and I came across dis question at work today...hadnt seen it since my university days. Anyone know the right answer? 

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 other 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 take the switch?   :thinking:

Offline trinindian

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Re: What are the odds...
« Reply #1 on: May 05, 2006, 03:10:01 PM »
Yes you switch because it increases the probability that you chose the correct door
 

Offline JayTheWrecker

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Re: What are the odds...
« Reply #2 on: May 05, 2006, 04:03:42 PM »
well, purely on the odds it makes no difference. There is a 50/50 chance that the car is behind Door 1 and 50/50 it's behind door 2

the thing is, there is a human element in this question, namely the game show host who knows which door has the car. If the car is behind Door 2, perhaps the game show host is trying to persuade the contestant to switch to Door 2 because he wants the contestant to win the big prize. However, there's also the chance that the host might be a sadistic shitbag and he trying to make the contestant pick the wrong door

if it was i, i would switch because the majority of game show host want the contestants to win
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Offline ndookie

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Re: What are the odds...
« Reply #3 on: May 05, 2006, 04:12:14 PM »
well , as trinindian said , it us better odds , from 33 % to 50 % , but on the other hand , depending on the game show , i would pick the door , cause i know if the host is a really a sadist..
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Offline Blue

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Re: What are the odds...
« Reply #4 on: May 05, 2006, 04:23:11 PM »
Ignoring the human element (which doesn't really change the answer, just the probability)...

trinindian is correct  :applause:

ndookie, i think u misinterpreted trinindian's answer.

If you switch boxes, the probability of winning increases to 67%. Anyone wanna explain why?  ;)
« Last Edit: May 05, 2006, 04:36:34 PM by Ryan »

Offline ndookie

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Re: What are the odds...
« Reply #5 on: May 05, 2006, 04:30:11 PM »
dam , yuh could excuse meh , i now learning quadratic formula an thing...

i jus realise that the man open door 3 rather than door 1 ...

something about this sounding like actural mathematics..

but i dont know..explain , you have me in suspense
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Offline Blue

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Re: What are the odds...
« Reply #6 on: May 05, 2006, 04:33:36 PM »
dam , yuh could excuse meh , i now learning quadratic formula an thing...

i jus realise that the man open door 3 rather than door 1 ...

something about this sounding like actural mathematics..

but i dont know..explain , you have me in suspense

actuarial.

no its not, its just probability. but i did study actuarial maths at uni  ;D

Offline ndookie

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Re: What are the odds...
« Reply #7 on: May 05, 2006, 04:37:53 PM »
so...anyone have the answer ?
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Offline ndookie

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Re: What are the odds...
« Reply #8 on: May 05, 2006, 06:07:13 PM »
weey , the man leave we without the answer..
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Offline trinindian

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Re: What are the odds...
« Reply #9 on: May 05, 2006, 06:48:52 PM »
lets start at the top
you have three doors each one has equal chance of been right
you pick one that and chances are that it is 33.3% correct
that mean there is a 66.6% that you are inccorect.
when one of the remaining doors is eliminated
the probability that you are wrong remains at 66.6%

therefore it makes sense to chose the door that was not chosen initally becasuse it will mean you have a 66.6 % of been right
« Last Edit: May 05, 2006, 07:03:46 PM by trinindian »
 

Offline Rastaman

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Re: What are the odds...
« Reply #10 on: May 05, 2006, 06:59:12 PM »
lets start at the top
you have three doors each one has equal chance of been right
you pick one that and chances are that it is 33.3% correct
that mean there is a 66.6% that you are inccorect.
when one of the remaining doors is eliminated
the probability that you are wrong remains at 66.6%

therefore it makes sense to chose the door that was onot chosen initally becasuse it will mean you have a 66.6 % of been right
That is why I failed A Level maths.

Offline lickslikefire

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Re: What are the odds...
« Reply #11 on: May 05, 2006, 07:00:35 PM »
wogoood maths...i'm a maths man too....... ;D

yeah the problem Ryan give is called the Monty Hall Problem...i also did actuarial science in uni  ;D

the answer is you always switch no matter what, because your probability of winning increases from 1/3 to 2/3..

First case: You choose a door randomly......the probability of winning is simply a 1/3....(one out of 3 doors)

Second case: You choose a door randomly and out of the 2 unchosen doors(remember the announcer knows the locations of the 2 goats and the car), the announcer always shows you a goat and gives you the option of switching doors....the question is should you switch?

think about it in scenarios to help yuh understand it:

Remember there is Goat1, Goat2, and a Car

Scenario 1: You initially choose Goat1
That means when the man show yuh a goat....and if you switch you have a 100% probability of getting a car

Scenario 2: You initially choose Goat2
That means when the man show yuh a goat....and  if you switch you have a 100% probability of getting a car

Scenario 2: You initially choose the car
That means when the man show yuh a goat....and  if you switch you have a 100% probability of getting a goat

moral of the story: switch doors since there is a 2/3 chance you will win the car if you switch  ;D



Offline lickslikefire

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Re: What are the odds...
« Reply #12 on: May 05, 2006, 07:04:31 PM »
lets start at the top
you have three doors each one has equal chance of been right
you pick one that and chances are that it is 33.3% correct
that mean there is a 66.6% that you are inccorect.
when one of the remaining doors is eliminated the probability that you are wrong remains at 66.6%

therefore it makes sense to chose the door that was onot chosen initally becasuse it will mean you have a 66.6 % of been right

i like yuh reasoning up till yuh said, "the probability that you are wrong remains at 66.6% "

i doh follow dat....it all about conditional probability breds....

Offline trinindian

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Re: What are the odds...
« Reply #13 on: May 05, 2006, 07:20:20 PM »
lets start at the top
you have three doors each one has equal chance of been right
you pick one that and chances are that it is 33.3% correct
that mean there is a 66.6% that you are inccorect.
when one of the remaining doors is eliminated the probability that you are wrong remains at 66.6%

therefore it makes sense to chose the door that was onot chosen initally becasuse it will mean you have a 66.6 % of been right

i like yuh reasoning up till yuh said, "the probability that you are wrong remains at 66.6% "

i doh follow dat....it all about conditional probability breds....


the probability must add up to one

based on you inital choice you have a  66 percet chance that your choice is wrong
and when the door is elimiated if you keep your first choice the probability that  your inital decision was wrong remains at 66%.
 

Offline lickslikefire

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Re: What are the odds...
« Reply #14 on: May 05, 2006, 07:32:59 PM »
lets start at the top
you have three doors each one has equal chance of been right
you pick one that and chances are that it is 33.3% correct
that mean there is a 66.6% that you are inccorect.
when one of the remaining doors is eliminated the probability that you are wrong remains at 66.6%

therefore it makes sense to chose the door that was onot chosen initally becasuse it will mean you have a 66.6 % of been right

i like yuh reasoning up till yuh said, "the probability that you are wrong remains at 66.6% "

i doh follow dat....it all about conditional probability breds....


the probability must add up to one

based on you inital choice you have a  66 percet chance that your choice is wrong
and when the door is elimiated if you keep your first choice the probability that  your inital decision was wrong remains at 66%.


I agree that "if you keep your first choice the probability that your inital decision was wrong remains at 2/3", but how does that imply anything about the probability of switching doors = 2/3....i don't follow that connection....

Offline trinindian

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Re: What are the odds...
« Reply #15 on: May 06, 2006, 12:23:24 AM »

 the probability that your inital decision was wrong remains at 2/3"



which mean there is a 2/3 probability that one of the doors the host has to eliminate is the correct one.When he reveals the door with a goat the probability of that door goes to zero, but the sum of the probability of both doors remain the same at 2/3, therefore the door that the host did not eliminate (and you did not chose) has a 2/3 in chance of being right. Therefore switch to the door with the higher probability  to increase your chance of winning.
« Last Edit: May 06, 2006, 09:23:08 AM by trinindian »
 

Offline Blue

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Re: What are the odds...
« Reply #16 on: May 06, 2006, 02:57:45 AM »
Great explanations - for anyone who doesn't belive the answer, try this => The Monty Hall Simulator - play it a few times before you draw any conclusions (no, the simulator isn't rigged  ;D).

« Last Edit: May 06, 2006, 03:00:37 AM by Ryan »

Offline ndookie

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Re: What are the odds...
« Reply #17 on: May 06, 2006, 09:19:46 AM »
does actuarial maths make sense doing ?

what kind of job do you get etc ?

i wont be surprised that i see this question in this years olympian..
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Offline lickslikefire

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Re: What are the odds...
« Reply #18 on: May 06, 2006, 09:42:50 AM »

 the probability that your inital decision was wrong remains at 2/3"



which mean there is a 2/3 probability that one of the doors the host has to eliminate is the correct one.When he reveals the door with a goat the probability of that door goes to zero, but the sum of the probability of both doors remain the same at 2/3, therefore the door that the host did not eliminate (and you did not chose) has a 2/3 in chance of being right. Therefore switch to the door with the higher probability  to increase your chance of winning.

ways I didn't think about it that way at all.......I like that reasoning 

yuh just had to break it down in lamens terms for meh breds  ;D

by the way, this is not related, but that pic yuh have scary brudda...yuh looking like a stalker/thirst man peeping behind a wall....please don't take offense  ;D...just thought I would inform yuh....

Offline lickslikefire

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Re: What are the odds...
« Reply #19 on: May 06, 2006, 09:50:07 AM »
does actuarial maths make sense doing ?

what kind of job do you get etc ?

i wont be surprised that i see this question in this years olympian..

way if yuh want to make real money I do not suggest this route...there's many ways to make more money....it's a common misconception in general that actuaries make real dollars....

don't get me wrong...they make higher relative to the average person..but they just have a lot better and more efficient ways in my opinion to earn more money....

however if yuh like studying exams(cause you will be studying for awhile), and yuh want a comfortable life(not 12 hour days and ting)..then it's not a bad route....it requires a lot of discipline though.....
and the exams hard no ass....

Offline ndookie

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Re: What are the odds...
« Reply #20 on: May 06, 2006, 09:54:03 AM »
for real , no offense though , you should have yuh entire face on it lol
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Offline ndookie

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Re: What are the odds...
« Reply #21 on: May 06, 2006, 09:59:13 AM »
if ah like studying exams ... wha kinda question is that ?

I never found there to be actual studying in mathematics..
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Offline trinindian

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Re: What are the odds...
« Reply #22 on: May 06, 2006, 10:08:04 AM »
by the way, this is not related, but that pic yuh have scary brudda...yuh looking like a stalker/thirst man peeping behind a wall....please don't take offense  ;D...just thought I would inform yuh....

well I had jus cut my hair off and i was trying an artistic thing that i saw, so  i cut the pic in half , but the chances are since i don't smile in my pics I go still look scary even in the whole. but the board has spoken and the verdict is i a'int no artist so according to dutty suggestion maybach it is
« Last Edit: May 06, 2006, 10:11:26 AM by trinindian »
 

Offline Blue

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Re: What are the odds...
« Reply #23 on: May 06, 2006, 10:08:58 AM »
does actuarial maths make sense doing ?

what kind of job do you get etc ?

i wont be surprised that i see this question in this years olympian..

The logical progression for some who does an actuarial maths degree is to become an actuary (which involves sitting further professional exams), although some of my classmates went into statistical jobs, banking and other finanical careers

Actuaries tend to work in the fields of insurance, pensions or investment - i'm over-simplifying greatly here, but they basically work out how much it is likely to cost to provide a future financial benefit. In Trinidad, all the major insurance companies have their own actuaries.

Salary-wise, actuaries do alright, and they are well respected so if you're good at maths its a pretty good profession to be in.

For more info on actuaries, see www.actuaries.org.uk (United Kingdom) and www.soa.org (North America)

PS - When I was in high school all I cared about was how much money I could make, so you could check dese links too  ;D North America and UK
« Last Edit: May 06, 2006, 10:12:38 AM by Ryan »

Offline ndookie

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Re: What are the odds...
« Reply #24 on: May 06, 2006, 10:15:19 AM »
thanks  ;D

money money money lol
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Offline lickslikefire

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Re: What are the odds...
« Reply #25 on: May 06, 2006, 10:20:12 AM »
if ah like studying exams ... wha kinda question is that ?

I never found there to be actual studying in mathematics..

also the actuarial exams yuh will be studying is not just maths...that's only for the preliminary exams...the main ones will be more insurance/pension/investment based......plenty memorization  ;D

Offline ndookie

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Re: What are the odds...
« Reply #26 on: May 06, 2006, 10:33:57 AM »
well i out dey lol

memorisation is not meh thing..lol
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Offline Pointman

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Re: What are the odds...
« Reply #27 on: May 06, 2006, 12:13:03 PM »
wogoood maths...i'm a maths man too....... ;D

yeah the problem Ryan give is called the Monty Hall Problem...i also did actuarial science in uni  ;D

the answer is you always switch no matter what, because your probability of winning increases from 1/3 to 2/3..
First case: You choose a door randomly......the probability of winning is simply a 1/3....(one out of 3 doors)

Second case: You choose a door randomly and out of the 2 unchosen doors(remember the announcer knows the locations of the 2 goats and the car), the announcer always shows you a goat and gives you the option of switching doors....the question is should you switch?

think about it in scenarios to help yuh understand it:

Remember there is Goat1, Goat2, and a Car

Scenario 1: You initially choose Goat1
That means when the man show yuh a goat....and if you switch you have a 100% probability of getting a car

Scenario 2: You initially choose Goat2
That means when the man show yuh a goat....and  if you switch you have a 100% probability of getting a car

Scenario 2: You initially choose the car
That means when the man show yuh a goat....and  if you switch you have a 100% probability of getting a goat

moral of the story: switch doors since there is a 2/3 chance you will win the car if you switch  ;D




what if you chose the correct answer(purely by luck) on the first pick. Why switch?
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Offline lickslikefire

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Re: What are the odds...
« Reply #28 on: May 06, 2006, 12:21:47 PM »
wogoood maths...i'm a maths man too....... ;D

yeah the problem Ryan give is called the Monty Hall Problem...i also did actuarial science in uni  ;D

the answer is you always switch no matter what, because your probability of winning increases from 1/3 to 2/3..
First case: You choose a door randomly......the probability of winning is simply a 1/3....(one out of 3 doors)

Second case: You choose a door randomly and out of the 2 unchosen doors(remember the announcer knows the locations of the 2 goats and the car), the announcer always shows you a goat and gives you the option of switching doors....the question is should you switch?

think about it in scenarios to help yuh understand it:

Remember there is Goat1, Goat2, and a Car

Scenario 1: You initially choose Goat1
That means when the man show yuh a goat....and if you switch you have a 100% probability of getting a car

Scenario 2: You initially choose Goat2
That means when the man show yuh a goat....and  if you switch you have a 100% probability of getting a car

Scenario 2: You initially choose the car
That means when the man show yuh a goat....and  if you switch you have a 100% probability of getting a goat

moral of the story: switch doors since there is a 2/3 chance you will win the car if you switch  ;D




what if you chose the correct answer(purely by luck) on the first pick. Why switch?

the thing is yuh won't know yuh choose the correct answer(cause it's a closed door).......so the question is asking if you would switch(assuming you do not know the result behind the door)

Offline Blue

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Re: What are the odds...
« Reply #29 on: May 06, 2006, 12:24:01 PM »
what if you chose the correct answer(purely by luck) on the first pick. Why switch?

Pointman, it's the probability of picking the correct one that the question is about.

You have no way of knowing whether you picked the correct one until the second door is opened. But your chances of winning increase if you switch. The key thing is that the presenter will always open a door with a goat behind it, regardless of whether you have picked the correct door in the first place or not.

 

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