Very Basic Probability: Lottery Chances If each ticket for a lottery has a 1 in 258,890,850 chance... what happens if you buy 10 tickets? 
Is it:


*

*A 10 in 258,890,850 chance?

*A 1 in 258,890,840 chance?

*A 1 in 25,889,085.0 chance?


What is the best way to represent the chances? This is very simple, but I can't figure it out.
 A: If you have a $1$ in $258,890,850$ chance to win with one ticket, that is a chance of $$\frac{1}{258,890,850} $$ then to find out what happens with $10$ unique tickets you simply multiply your chance with one ticket by $10$. Thus the chance to win becomes $$ \frac{10}{258,890,850}=\frac{1}{25,889,085}$$
Thus both your first answer and third answer are correct, and both would be acceptable ways to write the probability of winning with $10$ tickets.
A: Here's a simple way to look at it:
Suppose this is a Pick 6 lottery (it doesn't much matter the exact numbers),
and there are N possible sets of 6 numbers that can be chosen,
258,890,850 in your example.
Now suppose you buy 2 tickets: (1 2 3 4 5 6) and (7 8 9 10 11 12).
Each of those has a 1 in N chance of being the winner, and now you have a 
2 in N chance since that's how many sets of numbers you have.
And for any n tickets that you buy, you'll have an "n in N" chance of one of them being the winner.
In the extreme, if you buy N tickets, all different, you now have an N in N, or 100% chance of winning, which is fine if you can manage to buy all those tickets, the jackpot is bigger than N, and there is no chance you'll have to split the pot with another winning ticket.
