Conceptual question on Probability today I've stumbled in a interesting question about probabilities while talking to a friend, I don't know whether here is the best place to ask, but as it involves probabilities, I'll try.
Given a set of numbers $1,\ldots,N$ as a sample space in a lottery ticket, we have to mark a subset of $M$ numbers.
Why do we have a common sense that we have better chances choosing a sparse subset of numbers instead of a contiguous subset. Isn't the probability the same, or is there deeper math involved that I'm not aware of?
Thanks in advance.  

The probability of any number combination being drawn is exactly the same, assuming the lottery is fair (which it is virtually guaranteed to be). However, if you want to maximize your expected winnings, then you have to take into account how many people you split the prize with. If you choose 1,2,3,4,5,6 probably a lot of other people will choose this too so if you win you have to split the prize many ways so your expected winnings are significantly lower. So you should either choose randomly or try to figure out what number combinations are the least likely to be picked by other people.
