Soca Warriors Online Discussion Forum
General => General Discussion => Topic started by: Blue on May 05, 2006, 02:59:33 PM
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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:
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Yes you switch because it increases the probability that you chose the correct door
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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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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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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? ;)
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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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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
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so...anyone have the answer ?
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weey , the man leave we without the answer..
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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
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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.
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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
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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....
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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%.
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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....
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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.
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Great explanations - for anyone who doesn't belive the answer, try this => The Monty Hall Simulator (http://math.ucsd.edu/~crypto/Monty/monty.html) - play it a few times before you draw any conclusions (no, the simulator isn't rigged ;D).
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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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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....
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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....
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for real , no offense though , you should have yuh entire face on it lol
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if ah like studying exams ... wha kinda question is that ?
I never found there to be actual studying in mathematics..
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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
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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 (http://www.actuaries.org.uk) (United Kingdom) and www.soa.org (http://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 (http://www.actuaryjobs.com/salary.html) and UK (http://www.actuaries.org.uk/Display_Page.cgi?url=/careers/salaries.html)
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thanks ;D
money money money lol
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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
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well i out dey lol
memorisation is not meh thing..lol
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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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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)
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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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Ryan, let me ask you a question
lets say that just after Monty Hall opens the door and is about to ask the contestant if he wants to switch, the producer of the show receives an anonymous phone call warning that there is a bomb wired up to the engine of the car that is behind one of the two remaining doors. As a result, the studio is evacuated and the police eventually send in JayTheMechanic to find the car and dis-arm the bomb. So I walk into the studio and I see three doors, one of which is already opened showing a goat. What are the odds that the first door I pick is the one with the car behind it? and why are my odds of picking the correct door, greater than those of the contestant?
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hmm , technically , your chance would be 50/50 , lower chances of getting it correct..hmm
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Ryan, let me ask you a question
lets say that just after Monty Hall opens the door and is about to ask the contestant if he wants to switch, the producer of the show receives an anonymous phone call warning that there is a bomb wired up to the engine of the car that is behind one of the two remaining doors. As a result, the studio is evacuated and the police eventually send in JayTheMechanic to find the car and dis-arm the bomb. So I walk into the studio and I see three doors, one of which is already opened showing a goat. What are the odds that the first door I pick is the one with the car behind it? and why are my odds of picking the correct door, greater than those of the contestant?
Jay,
The probability of you selecting the correct door (with the car) is 50%
But the probability of the bomb being behind the door which wasn't chosen by the contestant is still 67%.
Unfortunately, you don't have this information, so the odds of you picking a door that blows up in your face are higher than if you had seen the first part of the game show. If you had the extra info, you'd be less likely to die. ;D
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so wait a minute ..
If he open the door to the car , it blow up ... how he supposed to disarm it now ?
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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.
Ryan, if I choose a door(say #1) and the host opens #3 with the goat, then there are 2 unknowns and the odds of me having chosen the correct door is 50%. Why is it to my advantage to switch? assuming I don't want the goat. ;D
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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.
Ryan, if I choose a door(say #1) and the host opens #3 with the goat, then there are 2 unknowns and the odds of me having chosen the correct door is 50%. Why is it to my advantage to switch? assuming I don't want the goat. ;D
Pointman,
Say you choose door #1 - at this point you dont know which door the car is behind. you've made a random choice, selecting one out of 3 doors, so the probability that you have selected the correct door is 1 in 3, or 33%. Simple.
Since the probability must add up to 100%, this also means that the probability that the car is behind either door #2 or door #3 is 2 in 3, or 67%. Lets think of these doors as belonging to the host - so the host has a 2 in 3 chance of keeping his car.
Now to the important part. There are 2 key things:
1. The host knows which door the prize is behind.
2. And, regardless of whether you initially selected the correct door or not, the host will always open one door with a goat behind it. In other words, the chances of him opening a door with a goat behind it are 100% - he is not selecting at random.
Because of this, the probabilitty that the car was originally behind one of the host's doors remains unchanged (i.e. - it is still 67%)
Another way to think of it
Sometimes its easier to think of this problem, if we use 1000 doors rather than 3.
So - 1 car, 999 goats.
Same situation - you pick a door. The host then throws open 998 of "his" 999 doors, showing u goats behind all of dem.
Now, keeping in mind that he did not select these doors at random - do you think it is more likely that the car is behind your 1 door (which you selected out of 1,000) or his one remaining door? :thinking:
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so wait a minute ..
If he open the door to the car , it blow up ... how he supposed to disarm it now ?
That is for Jay to answer, he is d mechanic ;D
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Ryan, i want to thank you for posting this thread, it really made me think. I can see the light now. As you say the key is that Monty Hall MUST open a door that shows one of the two goats. If the Contestant makes it his policy to automatically switch when giving the choice then there are only 3 possibly scenarios, and in 2 out of the 3 possible scenarios the contestant picks the one with the car, hence 66.66666 percent
say,
door 1= Car
door 2= Goat 1
door 3= Goat 2
Scenario 1. Contestant picks Door 1(Car). Monty opens either door 2 or 3. Contestant switches to 2 or 3 and loses
Scenario 2. Contestant picks Door 2(Goat1) Â Monty CANNOT open door 1 so HE MUST open door 3. Contestant switches to Door 1 and wins
Scenario 3. Contestant picks Door 3(Goat2) Monty CANNOT open door 1 so HE MUST open door 2. Contestant picks door 1 and wins
Ryan, I salute you  :beermug:
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Ryan, i want to thank you for posting this thread, it really made me think. I can see the light now. As you say the key is that Monty Hall MUST open a door that shows one of the two goats. If the Contestant makes it his policy to automatically switch when giving the choice then there are only 3 possibly scenarios, and in 2 out of the 3 possible scenarios the contestant picks the one with the car, hence 66.66666 percent
say,
door 1= Car
door 2= Goat 1
door 3= Goat 2
Scenario 1. Contestant picks Door 1(Car). Monty opens either door 2 or 3. Contestant switches to 2 or 3 and loses
Scenario 2. Contestant picks Door 2(Goat1) Â Monty CANNOT open door 1 so HE MUST open door 3. Contestant switches to Door 1 and wins
Scenario 3. Contestant picks Door 3(Goat2) Monty CANNOT open door 1 so HE MUST open door 2. Contestant picks door 1 and wins
Ryan, I salute you  :beermug:
understood...VERY GOOD THREAD RYAN...post some more stuff like this. ;D
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Ryan, i want to thank you for posting this thread, it really made me think. I can see the light now. As you say the key is that Monty Hall MUST open a door that shows one of the two goats. If the Contestant makes it his policy to automatically switch when giving the choice then there are only 3 possibly scenarios, and in 2 out of the 3 possible scenarios the contestant picks the one with the car, hence 66.66666 percent
say,
door 1= Car
door 2= Goat 1
door 3= Goat 2
Scenario 1. Contestant picks Door 1(Car). Monty opens either door 2 or 3. Contestant switches to 2 or 3 and loses
Scenario 2. Contestant picks Door 2(Goat1) Â Monty CANNOT open door 1 so HE MUST open door 3. Contestant switches to Door 1 and wins
Scenario 3. Contestant picks Door 3(Goat2) Monty CANNOT open door 1 so HE MUST open door 2. Contestant picks door 1 and wins
Ryan, I salute you  :beermug:
understood...VERY GOOD THREAD RYAN...post some more stuff like this. ;D
Jay ah feel you in the wrong profession...try teaching
Ah like how you break it down for us lesser folks to understand....
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that was a good explanation Jay..if we ent win de car..we could still curry up dem goat ;D
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that was a good explanation Jay..if we ent win de car..we could still curry up dem goat ;D
dem goat can go tobago an earn allya some money ;D ;D ;D ;D
Only you could come up with that kinda responce.....
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aye where you was hiding man
Righ let me buss the mark.....when no body else is online West Coast finds all the updated Threads and post on them....He does be real bored.... Right now it is 7:00 am here what time is it by you ???
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that was a good explanation Jay..if we ent win de car..we could still curry up dem goat ;D
only a Trini would think about making a trini cook after not winning the car ;D
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well wha yuh expect , yuh in a trini forum !
i for the curry goat !
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No..1 cause most likely d host playin wit yuh head
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that was a good explanation Jay..if we ent win de car..we could still curry up dem goat ;D
only a Trini would think about making a trini cook after not winning the car ;D
When Ryan say was either goats and cyar ah hadda think long and hard cause i woulda be satisfied with de goats and dem. curry goat oui ;D