Brain teaser

[Steve Axford]

Imagine a game show.
There are 3 doors, one with a major prize and the other two with a donkey behind.
You are asked to pick a door.
You pick one.
The host then opens another door - always revealing a donkey.
The host then asks you - do you want to change your pick?
Do you?

[fillum]

So I get either a "major prize" or a donkey? That's a win/win imo . But if I wanted the major prize I would change my pick.



Cheers.

[Steve Axford]

Why?
p.s. The donkey is an unfriendly donkey and bites - so you don't want him.

[fillum]

Why?
p.s. The donkey is an unfriendly donkey and bites - so you don't want him.

I could use him as a 'guard donkey'

[Cage]

Keep my pick.

The host opens 'another door' and 'always reveals a donkey' so has already opened both the doors with a donkey behind them.

Eeeaw, eeeaw, 'e always does that.

[jim]

I assume the door you picked isn't opened. So you change for improved odds.

[lay-z]

I'd always switch doors.
Stay with me here.
I've chosen my initial door (1) - that's a 1/3 chance of getting the prize.
The hsot reveals a losing door (door 3). Thus, Door 2 remains
IF I stick with my initial chosen door (1), I stay with a 1/3 chance of winning
IF I switch to the other door (2), I now have a 2/3 chance of winning.
Why? Because by the host revealing the donkey door, statistically speaking, there is a 2/3 chance of the prize being behind the remaining door.

[Ms Monny]

Alan, that just mashed my brain!!

I have read and re-read your answer and it still doesn't make sense! You have probably got the right answer though.

I would pick the door that is NOT next to the donkey!

[davidd]

I'd always switch doors.
Stay with me here.
I've chosen my initial door (1) - that's a 1/3 chance of getting the prize.
The hsot reveals a losing door (door 3). Thus, Door 2 remains
IF I stick with my initial chosen door (1), I stay with a 1/3 chance of winning
IF I switch to the other door (2), I now have a 2/3 chance of winning.
Why? Because by the host revealing the donkey door, statistically speaking, there is a 2/3 chance of the prize being behind the remaining door.

Actually I believe it is now 50% chance, there are now two doors, and one has a donkey, one has the prize, so there is an equal chance that your door or the other door has the prize.

I would probably stay with my original choice.

[jim]

Ms Money, try this. There are a thousand doors and after you pick one, the host will open 998 with donkeys. Same problem, but the answer's more obvious I think.

[jim]

Davidd you chose before the door was opened, so your odds haven't changed. Still one in three. They only change if you pick the other door.

[davidd]

Yeah, I wondered about that, but if you have the chance of changing your mind, you are effectively choosing again, so I would think it is now 50% each.

[Steve Axford]

My guess is that some of you have heard this before, because the answer is anything but intuitive. In fact, the more you know about probability theory, the less likely you are to get it right. I blew my mind when I first heard it, and I think in probabilities.
The doors haven't changed, but the host changed the rules by picking a door that wasn't random.

[Speedway]

The odds don't alter revealing all but 2 doors they are still 50/50 on the final decision.
Keith..

[Steve Axford]

Wrong

[ameerat42]

Look. Were any donkeys hurt in this joke? Nasty biters or not.

[Ms Monny]

my brain is certainly hurting, stuff the donkeys!!!!

[Ms Monny]

Yes, you change the pick because the host is giving you a clue that you have a donkey!! yes??? no??? oh, please tell us!!

[Steve Axford]

I sympathise Ms. My brain hurt when I heard this too. I made sense but didn't all at the same time. It took me a full day to make sense of it (and I mean make sense rather than calculate the correct answer).

[lay-z]

I'll come back from Lunch and do a drawing to explain it all.