Also, you forget that once you buy more tickets, the total amount of tickets sold will be larger. It comes down to whether this is a lotery where they draw a number from all possible numbers or a lottery where they guarantee someone is going to win. If you include the possibility of having the same number as somebody else it becomes different alltogether.
poss. 1 As explained above, your chances increase whith the factor of the amount of tickets you buy (buying 10 has a chance of winning of 10 times the probability when buying 1).
poss 2 Almost the same as poss 1, but a tiny bit less because the total amount of tickets sold also grows when you buy more tickets.
poss 3 Depends on how many people have the same number and whether there has to be a winner or not.
