The role of probability in solving the Monty Hall problem

[ErGingerbreadMandude]

Let me elaborate further rob.
I'm the host.
I have 3 doors in front of you.
Now choose one to open.

[robvalue]

Oh wait.

Ok, I pick door 1.

[ErGingerbreadMandude]

Oh wait.

Ok, I pick door 1.

So now I open door 3 for you.
You see a goat, I ask you if you want to change your option.

What do you do, why?

[robvalue]

I change door.

For all the reasons we've explained. Where is the lying coming in?

[ErGingerbreadMandude]

I change door.

For all the reasons we've explained. Where is the lying coming in?

For the reasons you've explained?
Would you agree that changing your option works in your favor than the other way around?

[robvalue]

Er... what?

I don't understand you. Yes, this whole thread has been explaining why you change.

The only assumption I make is that the prize has initially been selected randomly to be behind one of the doors.

If I chose wrong initially, with 2/3 chance, I will guarantee to win if I change.

If I chose right initially, with 1/3 chance, I will lose.

Chances I win = (2/3) * 1 + (1/3) * 0 = 2/3

It's how you calculate the mean of a probability distribution.

Sum(i=1..n)[i*Prob(X=i)]

[ErGingerbreadMandude]

Er... what?

I don't understand you. Yes, this whole thread has been explaining why you change.

The only assumption I make is that the prize has initially been selected randomly to be behind one of the doors.

If I chose wrong initially, with 2/3 chance, I will guarantee to win if I change.

If I chose right initially, with 1/3 chance, I will lose.

Chances I win = (2/3) * 1 + (1/3) * 0 = 2/3

It's how you calculate the mean of a probability distribution.

The math is all very fascinating rob, too bad you'll be returning home with a goat. The car was behind door 1.

[robvalue]

OK. How's the program coming? Why are you scared to run it if you're so sure you're right?

Where does the lying come in?

[ErGingerbreadMandude]

OK. How's the program coming? Why are you scared to run it if you're so sure you're right?

Where does the lying come in?

Look back in the thread you'll see Jenny mentioning it.

[robvalue]

Er... OK. I don't know where to look, I'll look later.

You're meant to open the door to show me if I win or not, I don't just take your word. You know that, right?

You should go study probability distributions. If you don't understand them, you won't understand this. Although this is a very simple example of one.