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.