[quote]tedro wrote:
No, but for some reason this is always a difficult concept for people to understand.[/quote]
Wait until we get to the airplane on a threadmill problem…
I get it now, that’s pretty cool. The 100 door problem explains the concept the best.
Whats the problem where you tip the elevtor door man and you only have 2 dollars left or something?
[quote]Regular Gonzalez wrote:
Imagine you’re on a game show, and you’re given the choice of three doors. Behind one door is a briefcase containing one million dollars, behind the others, goats. You pick a door, say #1, and the host, who knows what’s behind the doors, opens another door, say #3, which has a goat. He says to you, “Do you want to pick door #2?”.
The host is not attempting to trick you. He does the same thing every week.
Is it to your advantage to switch your choice of doors?
[/quote]
No.
[quote]pookie wrote:
Switching takes your chances from 1/3 to 2/3, so yes, switching is good.
[/quote]
After door #3 was open by the host his chances became 1/2.
What does that change if he picks door #2?
[quote]pookie wrote:
Not so because when you make your choice, there are three doors in play, not two. That later one door is opened does not change the fact that when you chose, you picked one out of three.
[/quote]
The host changes the state of the game by picking a door himself.
Must recompute odds after every change of state.
[quote]power_bulker wrote:
All I remember was getting this question on the final exam and writing:
“1/3 + 1/3 = 2/3”
and getting it right 
[/quote]
If you were a statistician you would be wondering why it didn’t equal 1 when you finished the problem.
state 1 – pick one out of 3: 1/3 + 1/3 + 1/3 = 1
sate 2 – pick one out of 2: 1/2 + 1/2 = 1
[quote]LIFTICVSMAXIMVS wrote:
pookie wrote:
Switching takes your chances from 1/3 to 2/3, so yes, switching is good.
After door #3 was open by the host his chances became 1/2.
What does that change if he picks door #2?[/quote]
If you have a choice of 4 multipe choice questions, you randomly pick an answer because you don’t know jack about that topic. The millionaire woman says " do you want to use a 50/50" so 2 of the other answers are crossed out. There is a 3/4 chance that the other answer besidse the one you picked is correct.
Right?
[quote]elano wrote:
LIFTICVSMAXIMVS wrote:
pookie wrote:
Switching takes your chances from 1/3 to 2/3, so yes, switching is good.
After door #3 was open by the host his chances became 1/2.
What does that change if he picks door #2?
If you have a choice of 4 multipe choice questions, you randomly pick an answer because you don’t know jack about that topic. The millionaire woman says " do you want to use a 50/50" so 2 of the other answers are crossed out. There is a 3/4 chance that the other answer besidse the one you picked is correct.
Right?[/quote]
No. It becomes 50:50 as soon as the choice becomes 1 out of 2.
If instead of taking away 2 choices she takes away one the odds become 1/3 to be right and 2/3 to be wrong. Changing your mind about which number to pick does not change the odds at all.
All probabilities must add up to 1 for every change of state.
Did you bother to read the Wiki?
to me it seems like theres a lot put on an assumption that the host would tell you that youd have won the million dollars if you picked it right, it doesnt matter. you know you dont have the goat if he opens the door to reveal one so you still have the same number of options.
i cant see how it makes any difference unless you picked the wrong door to start and its irrelevant because theres always 2 non prizes.
Read the 100 door example and see if it makes more sense. Say bob opened up all the doors except the one you chose (1) and the other door left (36). Wouldn’t it be more likely that 36 is correct vs the (1) you picked since that was 1/100 ?
[quote]elano wrote:
LIFTICVSMAXIMVS wrote:
pookie wrote:
Switching takes your chances from 1/3 to 2/3, so yes, switching is good.
After door #3 was open by the host his chances became 1/2.
What does that change if he picks door #2?
If you have a choice of 4 multipe choice questions, you randomly pick an answer because you don’t know jack about that topic. The millionaire woman says " do you want to use a 50/50" so 2 of the other answers are crossed out. There is a 3/4 chance that the other answer besidse the one you picked is correct.
Right?[/quote]
Damn, that’s an interesting application. It works assuming they always leave the answer you’re leaning toward, which seems to be the case. If it was random your odds would be back to 1/2.
[quote]wfifer wrote:
elano wrote:
LIFTICVSMAXIMVS wrote:
pookie wrote:
Switching takes your chances from 1/3 to 2/3, so yes, switching is good.
After door #3 was open by the host his chances became 1/2.
What does that change if he picks door #2?
If you have a choice of 4 multipe choice questions, you randomly pick an answer because you don’t know jack about that topic. The millionaire woman says " do you want to use a 50/50" so 2 of the other answers are crossed out. There is a 3/4 chance that the other answer besidse the one you picked is correct.
Right?
Damn, that’s an interesting application. It works assuming they always leave the answer you’re leaning toward, which seems to be the case. If it was random your odds would be back to 1/2. [/quote]
Well the host isn’t going to cross out the correct answer. The point is to get rid of two wrong answers to make the question easier.
But as for the question: yes. By switching answers, you would have a 3/4 chance of a correct answer (because you have a 3/4 chance of being wrong on the first guess). The original answer still has a 1/4 chance of being correct.
However, this wouldn’t work on the show, because I believe you have to use the “50/50” before you choose an answer on “Who Wants to Be a Millionaire”
[quote]LIFTICVSMAXIMVS wrote:
pookie wrote:
Switching takes your chances from 1/3 to 2/3, so yes, switching is good.
After door #3 was open by the host his chances became 1/2.
What does that change if he picks door #2?[/quote]
Argh.
Have you read the rest of the thread?
Let’s try one more way:
You pick one door out of three. Your door has a 1/3 chance of being right. The remaining group of two non-picked doors has 2/3 chance of being right, right?
You have 1 group of 1 door with 1/3 the chances and a second group of two doors with 2/3 chances.
The host asks you if you’d prefer the second group with 2/3 the chances instead of your current group with 1/3 the chances. To do that, he eliminates one of the bad doors from the second group and offers you to switch to the remaining one.
As a group, the remaining door and the opened one still have 2/3 of the chances of having the prize. That’s why you have two closed doors with one of them (your initial pick) having 1/3 chance of winning and the remaining door having 2/3 chance of winning.
If you still don’t get it, well program yourself a simulation and find out by running a few million trials. You’ll get: “not switching” wins 33.3% or the time, “switching” wins 66.6%. It’s a mathematical fact.
Try putting this in an html file, it runs the game 1,000,000 times and checks to see how many times you would win if you switched:
[quote]pookie wrote:
LIFTICVSMAXIMVS wrote:
pookie wrote:
Switching takes your chances from 1/3 to 2/3, so yes, switching is good.
After door #3 was open by the host his chances became 1/2.
What does that change if he picks door #2?
Argh.
Have you read the rest of the thread?
Let’s try one more way:
You pick one door out of three. Your door has a 1/3 chance of being right. The remaining group of two non-picked doors has 2/3 chance of being right, right?
You have 1 group of 1 door with 1/3 the chances and a second group of two doors with 2/3 chances.
The host asks you if you’d prefer the second group with 2/3 the chances instead of your current group with 1/3 the chances. To do that, he eliminates one of the bad doors from the second group and offers you to switch to the remaining one.
As a group, the remaining door and the opened one still have 2/3 of the chances of having the prize. That’s why you have two closed doors with one of them (your initial pick) having 1/3 chance of winning and the remaining door having 2/3 chance of winning.
If you still don’t get it, well program yourself a simulation and find out by running a few million trials. You’ll get: “not switching” wins 33.3% or the time, “switching” wins 66.6%. It’s a mathematical fact.
[/quote]
Pookie, please tell me you do not believe the wiki site. There are only two choices. In fact, there are always only two choices because the host will always eliminate one bad option.
Your computer program is wrong because you start with incorrect assumptions – that there are three choices – when in fact there are always only two.
[quote]johnnytang24 wrote:
Try putting this in an html file, it runs the game 1,000,000 times and checks to see how many times you would win if you switched:
Results:
[/quote]
There are only two options to choose from because the host always eliminates the bad one.
No, you start with 3 choices. The program acts exactly as the game show would, step by step.
[quote]johnnytang24 wrote:
No, you start with 3 choices. The program acts exactly as the game show would, step by step.[/quote]
I understand what you think is happening but it isn’t.
what is happening:
First pick – 1/3 + 1/3 + 1/3 = 1
second pick – 1/2 + 1/2 = 1
What you think is happening: second pick – 1/3 + 2/3 = 1
You assume that the other choice besides the one you made becomes 2/3 because the host eliminates one. That is incorrect because there are ONLY TWO choices. The question you need to ask is how did the other choice become 2/3. It would have to apply to both selections since both must have an equal weight of being correct and that cannot be because their probabilities need to add up to 1.
You are putting way too much thought into this and forgetting simple probability. That wiki is wrong.
The only way the probability will be 2/3 being right is if you get to make 2 selections from the get. You, in fact, do not get that option.