My favorite math problem

[skoti]

Ok, so I am a big fan of probability questions.

Some of you may have heard this problem before, but hopefully not...

Here we go:


You are on a TV Game show and the host gives you 3 doors to choose from, Door A, B, and C. Behind one of these doors is the $50,000 grand prize. The other 2 doors have nothing behind them.

You pick door A.

At that point the host opens door B, and shows you that nothing is behind that door. So, there is now door A and C left. One of those has 50K and the other has nothing. He gives you the option to switch your door from A to C.

The question is, should you switch to C? should you stay with A? or does it even make a difference?

 

[big jim]

If there is correct answer to this question I dont know it but I will stick to door A.

 

[MC MUSTANG]

There are two arguments to this; one is math and one is logic:
1. with three doors, there is a 1/3 chance of any one door being correct. Once one of the doors is open, then you now have a two thirds chance of being wrong; so switch.
2. Assuming that the game show host knows which door is correct, it is possible that he only asks to switch if the correct door is inially chosen; so stay...

I will never be on a game show...

 

[BlondeOnaBusa]

I would change to door C. I'm sucha risk taker.

 

[Rocket_Man]

Wikipedia "Monty Hall Problem" - it's all there - pretty interesting.

 

[99'busa]

Doesn't matter I would pick the wrong one either way

 

[Over_Easy]

Similar to what MC stated you go from a 1 in 3 chance of winning to a 1 in 2 chance of winning regardles whether you choose A or C. I don't see how there is a correct answer but maybe I'm missing something.

 

[GSXRFANN]

Even if you do have 2/3 chance, the money could still be in door A. It really doesn't matter. The odds are the same.

 

[Wag]

There are two arguments to this; one is math and one is logic:
1. with three doors, there is a 1/3 chance of any one door being correct. Once one of the doors is open, then you now have a two thirds chance of being wrong; so switch.
2. Assuming that the game show host knows which door is correct, it is possible that he only asks to switch if the correct door is inially chosen; so stay...

I will never be on a game show...

Not correct. Once one of the doors is open, your chances change from 1 in 3 to 1 in 2. It makes no difference if you switch from A to C or not. Whichever one you prefer, go for it!

--Wag--

 

[runeight]

What's the question again? Door B?

r8

 

[06BUSA]

After door B is opened. You now have a 50/50. Flip a coin for 50K.

 

[bigjohn141]

I looked it up on wiki like rocket man said. Wow that is deep stuff man.

 

[06limited1st]

So there is no 100% right answer but you have a greater chance of getting the $50K if you switch because the hose has already chosen a wrong door.. Crazy problem

 

[BlkDrgnZ28]

i would change my guess to door B!

 

[Wag]

So there is no 100% right answer but you have a greater chance of getting the $50K if you switch because the hose has already chosen a wrong door.. Crazy problem

You don't have a greater chance if you switch.

If you stay with A, you have a 1 in 2 chance that you're right.

If you switch to C, you have a 1 in 2 chance that you'll be right.

The odds are the same either way.

As a matter of fact, toss in an element of psychology and think on this:

1. You pick a door.
2. The guy shows you one of the other doors which is empty.
3. His intent is to give you the opportunity to change your guess BECAUSE (drum roll please) . . .

. . . he is trying to get you to change your guess because you originally picked the right one.

My opinion? Stick with your first guess ONLY because it doesn't friggin' matter anyway!

--Wag--

 

[Wrath]

AM -->

1326492[/ATTACH] AM]
There are two arguments to this; one is math and one is logic:
1. with three doors, there is a 1/3 chance of any one door being correct.  Once one of the doors is open, then you now have a two thirds chance of being wrong; so switch.
2. Assuming that the game show host knows which door is correct, it is possible that he only asks to switch if the correct door is inially chosen; so stay...

I will never be on a game show...

Not correct.  Once one of the doors is open, your chances change from 1 in 3 to 1 in 2.  It makes no difference if you switch from A to C or not.  Whichever one you prefer, go for it!

--Wag--

+1

 

[BlondeOnaBusa]

i would change my guess to door B!

That door had nothing behind it.

slappa99

 

[Lycan]

How many SLAPPA99! Would a monkey SLAPPA99! if a monkey could SLAPPA99!?

That one's for you BOB

 

[BlondeOnaBusa]

That would be 99 slappa99!

 

[jjmetheny]

Why would it matter if my door has the letter A on it or the letter C? It's still the same door.