Classic problem/riddle

[JollyGreen]

This is very old but it is also brilliant. If you know the answer try not to spoil it until a few people have had a chance to read it and try it out.

You are a contestant on a show and there are three boxes for you to choose from. One box has a set of keys to a Ferrari and the others have a carrot in. You get to choose box 1 2 or 3

Let's assume for the sake of argument (Jeff) that you choose Box 2. The box is chosen but NOT opened when the host who knows which box holds the keys, opens box 1 and shows you a carrot in it.

He then asks if you want to stick with your original choice of box 2 or if you want to swap box 2 for box 3?

Do you stick or swap and why?

[ps1967]

Switch boxes.

There is a scene from the movie '21' with this problem in it

http://www.youtube.com/watch?v=6Rl_p3JlSd0

[JollyGreen]

Thanks for the link, I was unaware of the use in the film

[NileVentures]

This is a classic Monty Hall problem from my A'level stats. If you do the Maths (or Math for any Americans around) you will see that if change your choice, you double your chances of winning.

Marcus du Sautoy explains it far better than I can:
https://www.youtube.com/watch?v=o_djTy3G0pg

[PeterLe]

Marcus is able to present Maths in such an interesting way. I wish he had been my teacher at school. I loved watching his programs. Again, it comes back to something I was saying in another thread. Something can initially appear to be 50:50 but when you delve down, it's not so clear cut.

NileVentures I think your a mathematician, it woul be interesting to hear how you approach the betfair markets, without giving away any strategy of course

[Iron]

Let's assume for the sake of argument (Jeff) that you choose Box 2.

Argument? Moi?

I don't argue, I merely like to explore issues.

But after that bout of Mugsitis that hit you this morning, I daren't do so again!

Jeff

[JollyGreen]

I first came across this puzzle in a sociology class at Uni in around 1983 I had previously done A level mathematics and one of my main subjects was Engineering Mathematics. I knew of the problem so when it was discussed in class I kept quiet and noted the other students. There were lots of mathematics students in the class but very few would accept the answer.

I had got to know the lecturer quite well as I was quite keen on the work of De Bono, as was he. After the lecture I asked if he would pass it to the Mathematics Lecturer and was pleased when he did.

Once again I sat and recorded the reaction and answers from other students. Many were Maths Wizards, far better than me and to a man they all sat there and argued with the answer. One guy spat the dummy and stormed out. There was no agreement reached you were either in the switch camp or the stick camp.

I would not be surprised if this type of situation still occurs today. It certainly makes you think.

[gazuty]

You swap, for the 2/3 chance. Keeping your original choice remains a 1/3 chance.

[NileVentures]

NileVentures I think your a mathematician, it woul be interesting to hear how you approach the betfair markets, without giving away any strategy of course

Good question PeterLe:
I'm actually an engineer = applied mathematician and a Civil Engineer at that. So my approach to trading reflects my training, i.e. always looking to do something new, often over engineered but with a focus on reducing risk. So when it does go wrong, it tends to be spectacular.

That reminds me of the Student Union bar joke:
Qu. What's the difference between an Engineer and a Doctor?
Ans. Doctors only kill one at a time

[PeterLe]

NileVentures I think your a mathematician, it woul be interesting to hear how you approach the betfair markets, without giving away any strategy of course

Good question PeterLe:
I'm actually an engineer = applied mathematician and a Civil Engineer at that. So my approach to trading reflects my training, i.e. always looking to do something new, often over engineered but with a focus on reducing risk. So when it does go wrong, it tends to be spectacular.

That reminds me of the Student Union bar joke:
Qu. What's the difference between an Engineer and a Doctor?
Ans. Doctors only kill one at a time

ha ha! thanks for the reply and good luck!

[MyOldGran]

If you do the Maths (or Math for any Americans around) you will see that if change your choice, you double your chances of winning.

I don't really agree.

The chance before was 33.3%.

Now it is 50/50.

So it doesn't matter if you stick with your original choice or change.

The chance from the outset was always 50/50.

[gazuty]

I don't really agree.

The chance before was 33.3%.

Now it is 50/50.

So it doesn't matter if you stick with your original choice or change.

The chance from the outset was always 50/50.

Well then you are wrong (as I often am, but not in this case).

The chance at the outset was not 50/50. It was 1/3, 1/3, 1/3.

By swapping your original choice you increase your probability to 2/3 because you are choosing two of the three original boxes. It doesn't matter that you "know" for certain one of the original boxes has a carrot. You already knew at the outset that if you got to choose two boxes the probability of one of them having a carrot was 1.

If you stick with your first choice you only have a 1/3 chance.

You can prove this very quickly.

If at the start you are allowed to pick two boxes what would happen.

Well you could get two carrots.

Or you could get a carrot and a ferrari.

Or you could get a Ferrari and a carrot.

So of the three outcomes, there is a one in three chance of getting two carrots and a two in three chance of getting a Ferrari and a carrot.

By swapping you are choosing two boxes.

Not 50/50.

[Wyndon]

Myoldgran is in some good company - but still wrong. In the book, 'The man who loved numbers' about Paul Erdos, an eccentric (but who probably published or co-authored the greatest number of maths papers ever) it says that even he couldn't get his mind around this and wouldn't accept it until he saw it 'proved' by a Monte Carlo simulation. The way I heard it explained was as follows. Pick a card from a full pack and place it face down on the table. The object is to select the queen of hearts. Now suppose you turn over 50 of the remaining 51 cards and the queen of hearts still has not appeared. Would you prefer to change cards in this case? I would.

[JollyGreen]

I did say it is a brilliant puzzle to make you think!!

[haichless]

So if I change my card can I still keep the carrot,if its not the queen of hearts?