Riddle Me This: A Statistic Problem

[Gesture Required Ahead]

Part of the problem is that the host knows what is behind each door. The host would not open the door with the car behind it.

I know. So I'm making the point that it doesn't really matter.

 

[BDMao88]

Only idiots open doors; create your own door.

For example...You wrote on my profile about forza..I add you and offer help...you don't play forza and play by your own tune aka door 1.

I delete you, you fuck off, I carry on as normal...created my own door.

 

[Wigy]

Monthy hall problem.

Always switch.

If you don't understand it do a table map of all the possible outcomes, you'll see switching increases your odds.

 

[Pan1cMode]

I know. So I'm making the point that it doesn't really matter.

But the point is it does matter. In switching doors you effectively gain an extra 33% chance of picking the right door, the odds become stacked in your favour.


EDIT:

Okay, let's walk through this completely. Lets just say (for simplicity sake) that doors 1 and 2 have a goat behind them and door 3 has the car (it doesn't really matter which door has which just using this to show the scenarios)


Not switching
You choose door 1; you lose
You choose door 2; you lose
You choose door 3; you win

Switching
You choose door 1, host opens door 2 and you switch to door 3; you win
You choose door 2, host opens door 1 and you switch to door 3, you win
You choose door 3, host opens either door 1 or 2 and you switch to the other door; you lose

Each of those scenarios has an equal probability of occurring. As you can see, if you switch 2/3 times you will be successful while if you stay only one out of 3 times you are successful.

 

[smokey]

Chance of goat on 1st pick = 2/3

Chance of goat on 2nd pick = 1/2

 

[Eldriken]

Chance of goat on 1st pick = 2/3

Chance of goat on 2nd pick = 1/2

Points for the Fast Times at Ridgemont High gif.

 

[Pan1cMode]

Chance of goat on 1st pick = 2/3

Chance of goat on 2nd pick = 1/2

Actually your chance of getting a goat on second pick is 1/3. Hence you have a 2/3 chance of picking a car second time round.

 

[CrimsonShadow]

Hmmmm ..

 

[xInfra Deadx]

No balls, no chance.

 

[Chongo]

You guys are idiots, fuck the car I want a goat.

 

[AK Gookus]

Do you plan on moving to Russia afterwards Chongo?

 

[CrimsonShadow]

Ok so the reason it's fuzzy is that everyone is explaining it wrong. Basically this all boils down to the chance of you picking the right door at the. start vs. the host revealing the right door via elimination.

If you make the wrong guess , he'll reveal the right door as your alternate choice by eliminating the other wrong one. The only way he can't do this is if you picked the right door to begin with, which only has a 1/3 chance of happening.

So basically 2/3 times he'll be helping you out.

 

[Relaxedstate]

Ok so the reason it's fuzzy is that everyone is explaining it wrong. Basically this all boils down to the chance of you picking the right door at the. start vs. the host revealing the right door via elimination.

If you make the wrong guess , he'll reveal the right door as your alternate choice by eliminating the other wrong one. The only way he can't do this is if you picked the right door to begin with, which only has a 1/3 chance of happening.

So basically 2/3 times he'll be helping you out.

That is a good way to look at it. The key implication is that he always will choose a door that has a goat in it since he knows. If he randomly chooses a door after you pick, then it actually wouldn't matter. Likewise, if he picked a door randomly only if you first guess was a car then the probablity would fluctuate (but eventually average out to 2/3).

 

[roosTakk]

It matters but I cant remember why

Source: I went to college once

 

[roosTakk]

For people having trouble visualising why you should switch doors, imagine there are 100 doors to choose from.

After choosing your door, the game show host opens 98 other doors and shows you the goat behind them, he then offers to let you switch. Switching is the much better option because you only had a 1/100 chance of correctly choosing the right door at the beginning. By switching you effectively get a 99/100 chance of choosing the right door.

The maths hold true for when their are only 3 doors.

How? You still have 50% chance? Theres 2 doors. One has the car one doesn't. He just increased your odds from 1/100 to 1/2

 

[CrimsonShadow]

How? You still have 50% chance? Theres 2 doors. One has the car one doesn't. He just increased your odds from 1/100 to 1/2

When you made the blind pick at the beginning, you only had a 1/100 chance of getting the right door.

Which means, when he eliminates all of the other wrong doors (because he knows where the right door is), there's a 99% chance that the door he leaves standing is actually right (since your first choice was likely wrong).

There's a 1% chance that you got it right on the first shot -- and that situation makes him only able to leave a wrong door as the other final choice. In the other 99 cases he's helping you out by leaving the right door as your alternate choice.

 

[roosTakk]

When you made the blind pick at the beginning, you only had a 1/100 chance of getting the right door.

Which means, when he eliminates all of the other wrong doors (because he knows where the right door is), there's a 99% chance that the door he leaves standing is actually right (since your first choice was likely wrong).

There's a 1% chance that you got it right on the first shot, which makes him only able to leave a wrong door as the other final choice. In the other 99 cases he's helping you out by leaving the right door as your alternate choice.

Yeah i get that, and you had it right in your first post...you still do not have a 99% chance tho is what I was saying

 

[Temjiin]

Best explanation.

Stick = 66% Goat. Change = 66% Car.

Source: @smokey

 

[CrimsonShadow]

Yeah i get that, and you had it right in your first post...you still do not have a 99% chance tho is what I was saying

You have a 99% chance of being wrong with your first guess. And after he eliminates that other doors, if your first guess is wrong then the 1 door he leaves behind will be right.

So that means that there's a 99% chance the the only door he leaves is correct. Which is why switching to it has 99% odds of being right.

There's a 1/100 chance that you were right with your first guess and the other door he leaves you as a final choice is wrong. So by staying with your original choice, there's a 1% chance that you win.

 

[Relaxedstate]

ALthough if MMH teleports in right after you select your first door (thus doesn't witness/know). Then he only has a 50% chance of guessing right between the doors.

 

[CrimsonShadow]

@roosTakk think of it this way:

When you dumb it down, there are only 2 possible outcomes in this whole situation:

1) You picked the right door up front -- so when the host eliminates all the other wrong doors except 1, and leaves that 1 other door standing, that door is wrong
2) You picked the wrong door up front -- so when the host eliminates all the other wrong doors, and leaves that 1 door standing, that door is right.

The odds of 1) are the odds of you picking a right door first; so 1/3 or 1/100
The odds of 2) happening are the odds of you picking a wrong door first; so 2/3 or 99/100

That's why it's always the safer pick to switch to what he leaves behind. Doesn't mean it's right, but the odds are higher.

 

[Big Pampering]

Ok so the reason it's fuzzy is that everyone is explaining it wrong. Basically this all boils down to the chance of you picking the right door at the. start vs. the host revealing the right door via elimination.

If you make the wrong guess , he'll reveal the right door as your alternate choice by eliminating the other wrong one. The only way he can't do this is if you picked the right door to begin with, which only has a 1/3 chance of happening.

So basically 2/3 times he'll be helping you out.

so basically it is not even a guess right?

 

[CrimsonShadow]

so basically it is not even a guess right?

For him it's not a guess. Either

1) You picked the right door, so he has to just chose a random door to leave standing, or
2) You picked the wrong door.. So he will eliminate the other wrong doors (since he knows where they are) and leave the right door standing.

So your odds of being right by staying put are the odds of you making the first guess correctly. And your odds of being right by switching are the odds that you got the first guess wrong and he's going to help you out by leaving only the right door behind.

 

[CrimsonShadow]

If he had the option of lying to you and eliminating the winning door, and you had to choose whether you believed him or not, then he wouldn't affect your odds at all and your chances switching or staying would be the same.

But since you know he's helping you out by only eliminating wrong doors, then in every case where you're wrong, he will leave you the winning door one as your 1 other choice. So he is helping you out most of the time.

 

[OZZYGUITAR]

You switch doors because it technically increases your probability. And lol I argued this for like half an hour with @OZZYGUITAR from the other side just to mess with him. As for an explanation, you technically have a greater chance of picking a goat at the beginning (2 out of 3) and in those scenarios you would have to switch doors. So it changes from a 1 out of 3 to a 2 out of 3 chance. @Relaxedstate

you are the worst kind of person