Suppose there are 3 doors. Two of them have goats behind them

It's because the host knows the content behind the doors.

There are n doors numbered 1, 2, ... n.

You choose one.

Monty Hall then opens every door except your chosen door and one other and all opened doors had a goat behind them.

You now have the option of switching to the other unopened door.

The probability of your original choice being the winner is 1/n.
The probability of winning if you switch is (n-1)/n.

>>7671522

Right, the host will never open the door that has the goat behind it so that increases the odds that the door the host didn't pick has the goat behind it.

>>7671514
>Where did the extra 0.166666666 come from?
It came from your misunderstanding of probability.

>>7671514
>(i.e. if you pick a goat with probability 2/3, then you won since he will reveal the other goat, you'll switch and have the luxury car).
>Hence the probability of winning if you always switch is 2/3 or 0.6666666

Nope, you don't know if you picked a goat or the car, so switching makes no difference whatsoever.
No matter which door the host picks after you pick one, he picks a goat, so your 50/50 chance of winning never changes.
It's 50/50 when you start, and 50/50 on through.

what the fuck guys
you either win the car or a goat
2 options
50/50
switch or not doesn't matter.

>>7671653
notsureiftrolling.jpg

>>7671653
If you actually have a doctorate and are working in Silicon Valley as your name implies I suddenly feel better about my own job prospects.

>>7671514
You either get a shitty sports car worth 50k$ or a goat. You literally cannot lose.

>>7671514
All you need to understand is that your first choice was probably wrong. That alone justifies switching.

I'm not even good at math and I understand this. You guys debate this shit endlessly and there's nothing to debate. You probably chose a goat on your first pick since there's 2 and only 1 car, he shows the other goat, you should switch because that door probably has the car. The end. That's all there is to it.

Each door has 1/3 chance. Theres your door and the two other doors. So your door has 1/3 and the other two doors combined have a 2/3 chance. Even though the host opens one, as a group, the remaining doir retains the 2/3 chance.

So the 1/2 chance never existed. The 0.16666... never went anywhere.

>>7671653
Nope. When there were 3 doors to choose from, there were 2 goats and 1 car. If your strategy is to always switch, then picking a goat will mean you've won and picking a car will mean you've lost. The probability of picking a goat is 2/3. Hence your probability of winning given that your strategy is to switch is 2/3, not 1/2.

We can also look at it another way. Lets say its door 1, 2 and 3. Doors 1 and 2 have goats. Door 3 has a car. So lets look at all our possibilities if your strategy is to always switch.

Possibility 1: You pick door 1. Then the host has to open door 2. Then you switch to the car and win.

Possibility 2: You pick door 2. Then the host has to open door 1. Then you switch to the car and win.

Possibility 3: You pick door 3. Then the host can pick doors 1 or 2. Either way, you'll switch to the one he didn't pick and lose.

There are 3 possible outcomes and two of them count as a win. Hence the probability is 2/3.

>>7671684
If you wanted a goat, you would stick with the door you chose.

>>7671514
Statistics! Yay! I remembered coming across this problem at one point but I'm drunk and horny so I'm gonna go alone a cigarette jack off and sleep my misery away

>>7671514
If I win the goat, can I do *anything* with it?

>>7671915
Yes but that *anything* is illegal in 48 states. You better be in one of those two states.

>>7671917
Why would using it to control your lawn be illegal?

>>7671932
You sick sick man you want to mowq your grass with it?

I thought you just wanted to fuck it.

>>7671514
Whats wrong with winning a goat? you save on gas, goats make milk, cheese, and eggs (based on that goat project from the food network dude with the show, good eats), and when the goat gets old you can eat it!
Goat > Car

>>7671514
The prob you pick the car at the beginning is 1/3.

From here, it doesn't matter what goat door the host opens because it doesn't change the fact that you had a 1/3 chance to pick the door with the car.

1-1/3=2/3 chance the car is behind the other door.