h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

The 'disappearing money' thread reminded me of an oldie but a goodie - the donkey problem.


You are on a game show. You are shown three closed doors. Behind one door is a pot of gold. Behind each of the two other doors is a donkey.
You are asked to pick a door to try and pick the gold. You make your choice, then immediately one of the other doors is opened to reveal a donkey.

You are now offered the chance to change your mind and pick another door. Do you stick with your door, or change your mind? Or does it make no difference?

oh no, not monty hall again . . .
my brain hurts

Sorry Spinks, but this one has been rather done to death

A1138655

You're joking, aintcha?
Oh well, at least, er, new people can see it for the first time.

Okay, what about the oil drop problem?

Glass A contains only oil, and glass B contains only water.
A tablespoon of oil from glass A is put into glass B, and glass B stirred until it is well mixed. Then, a tablespoon from glass B mixture is taken and put into glass A.

Is there now more oil in glass B than there is water in glass A, or is it the same?

It's only four days since Monty Hall appeared on the front page, so they'll have to be very new people.

I'd not heard of Monty Hall. I thought it was by Maria Vos Savant.

There should be the same amount of oil in glass B as there is water in glass A, shouldn't there?

Oil and water don't mix. At all. But I can't remember which is lighter (oil, I think), so I can't answer the question.

Actually, Amy, because they don't mix you should be able to answer the question. It doesn't matter which is lighter.

2 things, what's monty hall?

And 2, who in their right mind puts 2 donkeys behind doors? I mean, donkeys? Benhind doors? Eh?

Cat

Well it might be worthwhile in any case...if you get to keep the donkey.

Cat Eyes, follow the link in Posting 3 to find out about Monty Hall.

I think its the same amount, half a table spoon each. But I'm probly wrong.
*sighs*

Yes, If you forget about oil and water not mixing then the amount is the same. Many reason that as the first teaspoon was pure oil and the second was a mixture then there's more oil in water.

Suppose there are five tablesoons in each glass...

1. Remove 1 tablespoon of oil from glass A and put in glass B. Glass A now contains 4 tablespoons of oil. Glass B contains 5 tablespoons water + 1 tablespoon oil.

2. Mix well.

3. Remove a tablespoon of liquid from glass B. This tablespoon will be 5/6ths water, 1/6 oil.

4. Place this tablespoon in glass A.

5. Glass A now contains 4 1/6 tablespoons oil, + 5/6 tablespoons water.

6. As the overall volumes of oil and water cannot have changed, the remaining quantities must be in glass B. As we started with 5 tablespoons of water, and 5/6ths of a tablespoon of water are now in glass A, there must be 4 1/6th tablespoons of water in glass B. Similarly, as there is 4 1/6th tablespoons of oil in glass A, there must be 5/6 tablespoon of oil in glass B.

The quantities are the same!

Great explanation Reddy, but am still completely baffled by two things: What is the answer to the dokey riddle, and who the F~@k is Monty Hall?!

Answers on a postcard please

Hmmm... donkey or gold? Methinks I'd rather have the donkey, it'd be something novel to keep in my room at uni! A good talking point, and a bit more original than the old stolen road signs!

>>What is the answer to the dokey riddle, and who the F~@k is Monty Hall?!

See posting 13.

Thanks Gnomon

Have just read through the liknk in post 3, and all the related links around the issue. Am still not convinced either way on the Monty Hall problem as both argumetns seem to make sense when viewed independantly of one another.
Bit of a head-f?@k, real interesting stuff though!