lutzj wrote:Yeah, I'm pretty sure your odds are just as good when buying ABCDE and ABCDF as when you buy ABCDE and FGHIJ, since the sequences of numbers are all unique and have an equal chance to pop up.
Let's say there are 2 letters drawn from 4, A B C and D.
The possible combinations are
Or 6 possibilities.
All letters have a 3/6 chance of being on the winning ticket.
You buy ticket AB. It is not the winning ticket.
The possibilities are now
Given this, A has only a 2/5 chance of being on the winning ticket, as does B. But C has a 3/5 chance, as does D. Wait, this can't be right. Looks like a paradox. CD has just as much chance of winning as AC, given AB doesn't win. Hmm. The winning ticket might have only a 2/5 chance of having A, but there are 2 ways to have A on the ticket, while 3 ways for C, so the odds all come out to be 1/5. Yeah, assuming that you must get all 5 numbers to win (no prize for 4 out of 5), knowing something about the losing ticket doesn't tell you anything about which one will be the winning ticket.