A maths problem (2).

[pete]

A brain teaser for you. No googling.

You are in the final of a quiz show, in which I am the quiz master.

The final is easy, there are 3 boxes (1, 2 and 3). In one box is a cheque for a million pounds the other two are empty.

You have to pick a box at which point I remove one of the 2 other boxes and tell you that the money is now in one of the remaining 2 boxes. (I have removed an empty box).

Should you change your mind.

What are the odds of your box having the money in it?

[renmure]

Yes you definately should.
I can't remember why, but I do remember deciding to remember the correct answer
Perfect answer, as long as you don't have to show the working out bit

[cla5h]

I think for me as an individual given one shot, then it makes no difference. Either my first choice has the cheque or it doesn't.

However, assuming the test is to be run many times, then has the probibility changed? In my initial choice I had a 1 in 3 chance of being correct. Now, given that I have a free choice of two boxes, the probability must have increased to 1 in 2 as a minimum.

Does the fact that a known empty box has been removed alter that further - I suspect so, but can't quantify it!

[flyingscot68]

Yes you definately should.
I can't remember why, but I do remember deciding to remember the correct answer
Perfect answer, as long as you don't have to show the working out bit

I remember seeing Derren Brown explain this when I went to see him live. Can't remember why but the answer was that the odds are shorter if you change your mind.

[pete]

Yes you definately should.
I can't remember why, but I do remember deciding to remember the correct answer
Perfect answer, as long as you don't have to show the working out bit

I remember seeing Derren Brown explain this when I went to see him live. Can't remember why but the answer was that the odds are shorter if you change your mind.

I didn't know Mr Brown did it! Ah well.

RAMTOP is right. The chances at round 1 are 1/3 that you get the right box.

in the second round the odds that the money is in your box (phnarr) is still 1/3 but the chances that the money is in the other remaining box is 1/2. So you should swap.

[jason]

I didn't know Mr Brown did it! Ah well.

I'm afraid just about every maths/conundrum presenter on TV has done it the past few years, Pete


It's a good one though, and a tricky one to 'click' until you recognise that the original box is always 2/3 likely to be wrong - even after a box has been removed, because the choice was made out of 3. However, the offered alternative (after one box is removed) is always 1/2 likely to be wrong/right.

[pete]

I didn't know Mr Brown did it! Ah well.

I'm afraid just about every maths/conundrum presenter on TV has done it the past few years, Pete

Oh FFS. (Roofer did some work last year and proudly brought in the TV aerial, claiming it wasn't doing anything. It was and we've never really got round to putting it back on the roof. We only get 3-4 channels, depending on the weather, and they don't seem to be very good.)

[jason]

I didn't know Mr Brown did it! Ah well.

I'm afraid just about every maths/conundrum presenter on TV has done it the past few years, Pete

Oh FFS. (Roofer did some work last year and proudly brought in the TV aerial, claiming it wasn't doing anything. It was and we've never really got round to putting it back on the roof. We only get 3-4 channels, depending on the weather, and they don't seem to be very good.)

In that case, there's a chance I can guess the odds that you missed them then. In all probability.