See If You Can Answer This Question Anot
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Hi,
This question was correctly answered by the person with the world's highest IQ according to Guiness Book of Records, so if you can figure it out, maybe you are not too far behind. Please dont cheat or if have heard the answer before, please let others play first.
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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 number 1, and the host, who knows what's behind the doors, opens another door, say number 3, which has a goat.
He says to you, "Do you want to pick door number 2?"
Is it to your advantage to switch your choice of doors?
Please explain why you agree or disagree to switch doors. -
No, You wants you to switch doors because Door 2 is a Goat but most people would think that the host has the same mentality as you and thus makes you believe that Door 2 is a goat but in fact it is a Car, Then again this is a simple mentality which he would already have cracked hence but changing your choice when he asks you to is a no no
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Switch. Preivously, the chances of ur chosen door is 1/3. However, now the chance is still 1/3, but the chances of the car in the other door is increased to 2/3, so switch ...
The answer is some thing like tt ... -
Got confused.
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yr answer is in the question....
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erm. i dont remember answering this questionOriginally posted by Li Ka Shing:This question was correctly answered by the person with the world's highest IQ according to Guiness Book of Records -
i think no matter what u say, the host will open another door that has a goat inside.
let say u choose door 1, he will open the 3rd door. cos he 3rd door is his 1st door.
then if u say 2nd door, if inside is a goat, he will open. if not, he will say something like u want to keep door 2. then ask u to open another door.
so no matter what, u won't win the car.
this is what i think.
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Goat or car, you still win something. Just a matter of how fast you want to get to your destination.
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goat can eat, car cannot.
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I forgot to mention to focus on logic/ maths/ probabilities, that means disregard other things like the host deliberately trying to trick you, etc like that.
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is the question complete ? ...
I remember this example being given in my probabilities class ....
after the prompting, shouldn't the host open one of the gates that doesn't contain a car behind ... and then ask the contestant again if he wants a switch, after the contestant has seen a door NOT containing the prize ...right ?
it's Called, Monte or Monty Hall's problem or something .... -
Yes the question is complete/ original.
Just play, unless if you have heard the answer, let others play first. -
right ... I'll hold my peace ... have fun guys ...Originally posted by Li Ka Shing:Yes the question is complete/ original.
Just play, unless if you have heard the answer, let others play first. -
The Monty Hall problem
This problem has rapidly become part of the mathematical folklore.
The American Mathematical Monthly, in its issue of January 1992, explains this problem carefully. The following are excerpted from that article.
Problem:
A TV host shows you three numbered doors (all three equally likely), one hiding a car and the other two hiding goats. You get to pick a door, winning whatever is behind it. Regardless of the door you choose, the host, who knows where the car is, then opens one of the other two doors to reveal a goat, and invites you to switch your choice if you so wish. Does switching increases your chances of winning the car?
If the host always opens one of the two other doors, you should switch. Notice that 1/3 of the time you choose the right door (i.e. the one with the car) and switching is wrong, while 2/3 of the time you choose the wrong door and switching gets you the car.
Thus the expected return of switching is 2/3 which improves over your original expected gain of 1/3.
Even if the hosts offers you to switch only part of the time, it pays to switch. Only in the case where we assume a malicious host (i.e. a host who entices you to switch based in the knowledge that you have the right door) would it pay not to switch.
There are several ways to convince yourself about why it pays to switch. Here's one. You select a door. At this time assume the host asks you if you want to switch before he opens any doors. Even though the odds that the door you selected is empty are high (2/3), there is no advantage on switching as there are two doors, and you don't know thich one to switch to. This means the 2/3 are evenly distributed, which as good as you are doing already. However, once Monty opens one of the two doors you selected, the chances that you selected the right door are still 1/3 and now you only have one door to choose from if you switch. So it pays to switch. -
Well thank you to bring a formal close to the game, I thought it can last a bit longer.
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sorry ... I shouldn't have mentioned the name ...Originally posted by Li Ka Shing:Well thank you to bring a formal close to the game, I thought it can last a bit longer. -
I have seen this explanation in the US show Numbers.Originally posted by anhydrouscoppersulphate:The Monty Hall problem
This problem has rapidly become part of the mathematical folklore.
The American Mathematical Monthly, in its issue of January 1992, explains this problem carefully. The following are excerpted from that article.
Problem:
A TV host shows you three numbered doors (all three equally likely), one hiding a car and the other two hiding goats. You get to pick a door, winning whatever is behind it. Regardless of the door you choose, the host, who knows where the car is, then opens one of the other two doors to reveal a goat, and invites you to switch your choice if you so wish. Does switching increases your chances of winning the car?
If the host always opens one of the two other doors, you should switch. Notice that 1/3 of the time you choose the right door (i.e. the one with the car) and switching is wrong, while 2/3 of the time you choose the wrong door and switching gets you the car.
Thus the expected return of switching is 2/3 which improves over your original expected gain of 1/3.
Even if the hosts offers you to switch only part of the time, it pays to switch. Only in the case where we assume a malicious host (i.e. a host who entices you to switch based in the knowledge that you have the right door) would it pay not to switch.
There are several ways to convince yourself about why it pays to switch. Here's one. You select a door. At this time assume the host asks you if you want to switch before he opens any doors. Even though the odds that the door you selected is empty are high (2/3), there is no advantage on switching as there are two doors, and you don't know thich one to switch to. This means the 2/3 are evenly distributed, which as good as you are doing already. However, once Monty opens one of the two doors you selected, the chances that you selected the right door are still 1/3 and now you only have one door to choose from if you switch. So it pays to switch. -
so whats the qn?
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things like this are solved with mathematical theories like probabilities and matices.
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is the calculations below correct?
(1) P(1st guess is right, and i choose not to switch)
= 1/3
if i choose to switch:
(2a) P(1st guess is wrong, but i switched to the correct door)
= P(1st guess is wrong) x P(i switched to the correct door)
= 2/3 x 1/2
= 1/3
(2b) P(1st guess is right, and i still switched to the correct door)
= P(1st guess is right) x P(i switched to the correct door)
= 1/3 x 1/2
= 1/6
(2c) P(i guess the right door)
= (2a) + (2b)
= 1/3 + 1/6
= 1/2 ----> which is greater than in (1)
so no matter whether my 1st guess is right or wrong, the probability of getting the right door if i choose to switch is higher. -
I won't switch doors.Originally posted by Li Ka Shing: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 number 1, and the host, who knows what's behind the doors, opens another door, say number 3, which has a goat.
He says to you, "Do you want to pick door number 2?"
Is it to your advantage to switch your choice of doors?
Please explain why you agree or disagree to switch doors.
Going by mathematical calculations, the chance of getting the car is
1/3 x 1/2 = 1/6
Chance of getting a goat is 1/3 x 1/2 = 1/6
Since both have equal chances, means that the car is either behind or not behind the doors. Depends on how optimistic you are lor. -
doesnt matter becaos it is the same. he already opened 1 door means 2 left. your chances are 1/2. There is only 2 doors and 1 door has a car. in fact the guy is helping u by eliminating 1 door.
anything narrowed down to 50/50 is luck....
anything narrowed down 1 chance is also luck. -
yup it's luck
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Actually, I also thought the same thing as you did. Your logic is right if there are only 2 doors and given 1 try, the chance will be 50/50. But due to the added step that initially there are 3 doors, then the situation has changed tremendously. The initial chance of you getting it right is 1/3 only. Opening 1 of the door doesn't change the fact that your probability of getting it right is still 1/3, but it does make you feel that the chance is now 1/2. So if you did make a switch, you indeed has a better chance. This question is tricky, got me too but after some thoughts, it does make sense now.Originally posted by Saint Valentine:doesnt matter becaos it is the same. he already opened 1 door means 2 left. your chances are 1/2. There is only 2 doors and 1 door has a car. in fact the guy is helping u by eliminating 1 door.
anything narrowed down to 50/50 is luck....
anything narrowed down 1 chance is also luck. -
haha... but my friend told me last time on tv got this guy really tried to eat the whole car, and he succeeded in doing so, I was really skeptical but I do believe such things can be done because... I've seen people eating metal nuts and bolts, I've seen people swallowing glasses, so what is stopping people from eating a car? I still prefer my juicy sirloin steak...Originally posted by SingaporeMacross:goat can eat, car cannot.