Probability Puzzle

[Andy Millne]

There are three cups. Under one cup there is a £100 note and under the other two is a 1p coin.

I know which cups hold what. You must pick one of the three cups at random. Before revealing whats underneath this cup, out of the remaining cups, I must select one of the cups with a 1p coin and remove it. If both of the cups have 1p I must remove one at random.

I now give you a chance to change your mind between the remaining cups.

Should you change your mind or not?

[Guest mrsvic]

There are three cups. Under one cup there is a £100 note and under the other two is a 1p coin.

I know which cups hold what. You must pick one of the three cups at random. Before revealing whats underneath this cup, out of the remaining cups, I must select one of the cups with a 1p coin and remove it. If both of the cups have 1p I must remove one at random.

I now give you a chance to change your mind between the remaining cups.

Should you change your mind or not?

So I believe, the odds increase of finding the £100 if you switch... from 1/3 to 1/2... the 1p will be your reward if you switch from choosing a £100 cup, but there is only a 1/3 chance of that happening... if you have chosen the 1p as your first choice, there will still be a £100 when you switch, 1/2 chance...

I get confused working out the odds on deal or no deal mind...

[Monsta®]

wey thats more of a con than the national lootery!

[Andy Millne]

So I believe, the odds increase of finding the £100 if you switch... from 1/3 to 1/2... the 1p will be your reward if you switch from choosing a £100 cup, but there is only a 1/3 chance of that happening... if you have chosen the 1p as your first choice, there will still be a £100 when you switch, 1/2 chance...

I get confused working out the odds on deal or no deal mind...

Well on theory the chances on deal or no deal should be 1 in however many boxes there are (I don't remember how many)

BUT....

does the banker know what's in the boxes? It is never actually stated to my knowledge that the banker doesn't know. I know the boxes are sealed but is that just for the benefit of the contestants and the host. Yes there is also the spiel that boxes are chosen at random by the contestants but, if the banker is aware what's in them, and his bank balance is a little low he may only give the option to switch if the lower value is in the contestants chosen box. Another way to ensure that the game is a little more controlled than we first assume?

[Guest mrsvic]

Well on theory the chances on deal or no deal should be 1 in however many boxes there are (I don't remember how many)

It's the more complecated bit like the probablity of getting the £250000 in the next 3 chooses when 8 boxes remain etc... I can never remember whether to add or multiply the probability on each box... if that was it...

Noel says at the beginning of each game that the only person who knows what is in each box is the independant adjudicator... which would have been believable until the game where the priest found a box with nowt in it... hmmm...

[threegee]

I think the problem here is that the human mind tightly associates the two events, whereas they are in fact two quite seperate ones. The way this problem is framed reinforces that association - but quite misleadingly.

We all know that the chances of getting the £100 are 1 in 3. Nothing post selection is going to change that. But here we are being given the opportunity of throwing away that selection as if it never happened. It's one we'd be silly to decline.

Yes, we COULD be throwing away the prize, and yes we are have no option but to select what is presented to us IF we are to change. But if we don't change we stick with those 1 in 3 odds. If we do change we have reduced the odds to 1 in 2.

It's simply an irrelevant reordering of events: Say one of the 1p cups was taken away before the selection. Our chances would then clearly be 50:50. The person taking away the cup isn't playing against us, he's constrained in "winding back the clock" to that 50:50 situation for us, by always removing one of the 1p cups.

Maybe the mental block is that we are constrained in the swap to taking what is given. But "taking what we are given" is still a random choice, because our first choice was a random choice. That's the only way the two events are linked.

[mobius]

Should you change your mind or not?

Yes, you should swap. This is a well known puzzle, commonly called the Monty Hall Problem

[Malcolm Robinson]

How does switching improve your chances? 2 doors 50/50 aint it????????

[Hamburger Pimp]

The chances of success are 1 in 3 if you stay with your first choice and 2 in 3 if you switch.

Try it for yourself

[Monsta®]

There are three cups. Under one cup there is a £100 note and under the other two is a 1p coin.

I know which cups hold what. You must pick one of the three cups at random. Before revealing whats underneath this cup, out of the remaining cups, I must select one of the cups with a 1p coin and remove it. If both of the cups have 1p I must remove one at random.

I now give you a chance to change your mind between the remaining cups.

Should you change your mind or not?

no you should not as you have mentioned the two unpicked cups have pennys under them! so obviously you have already won!