# Math Help - Apparent lottery anomaly

1. ## Apparent lottery anomaly

Hello, my name's Phil and as I’m sure you realise I’m new here. Although far from a mathematician I do have an interest in things mathematical, and hence am here to try, amongst other things, to resolve the following question. This relates to the UK lottery. It’s not something I take part in, never the less one aspect puzzles me. Although all the balls are numbered, they are also grouped in to four different colours. Now the theory is that during the draw any one of the balls stands an equal chance of being drawn – which would seem to make sense. But the fact that they are divided into four colour groups, seems to me, to complicate matters. Let us suppose the numbers 1 to 12 are blue, and that the first 5 to be drawn are all blue leaving 7 blue balls and all other colours untouched. Logic would seem to suggest the chances of drawing another blue ball are much reduced, and hence any of the numbers associated with that group? But this obviously contradicts the idea of equality for all numbers? I’m assured by smarter people than I that I’m wrong, and that may well be the case, but I still can’t see how. Is there a way of presenting this mathematically, or otherwise that can clear up this apparent (to me) contradiction? Thank you for your time.
Phil.

2. ## Re: Apparent lottery anomaly

I'm not sure what you mean by "the idea of equality for all numbers". Initially all numbers are equally likely to be chosen. But, obviously, after some have been chosen, those numbers cannot be drawn again. When you start, if there are the same number of blue balls as of other colors, then all colors are equally likely. However, after drawing some, while the individual balls that are left are "equally likely" to be chosen, if there are now fewer blue balls, a blue ball is now less likely to be chosen.

3. ## Re: Apparent lottery anomaly

Breaking it down a little further, with 5 blue balls removed let us suppose that the number 10, coloured blue, is still in play. Because it is part of the set of all remaining numbers it stands equal chance of being drawn as any other number. However, because it is also part of the set of blue balls, and there are now a reduced number of blue balls compared to the other colours, it appears to stand less chance of being drawn. The number 10 blue ball seems to be in two states of probability at the same time?