I see we're doing part 2 with different assumptions. I asume that once a player wins, all his tickets are removed from the ticket pool.
This is not for an exercise. I was bored and wanted to calculate my chances to win a beta key to some game
They allow you to have a total of 5 'tickets' and the widget also shows the amount of submitted tickets.
I asume, since it's a computer system deciding the winners, that a player's tickets are removed from the pool once the player has won something.
Ofcourse the probability is different once you assume that only the winning ticket is removed from the pool.
The 5% is very inacurate due to me rounding numbers here and there.
I do expect a number below your mentioned 7% since you're 1 out of ~286 players compared to you having 1 out of each 200 tickets (or me in this case).
PS. The 1000 and 3.5 are fictional numbers. In reality there are now 13k tickets in the pool with probably an average of 4.5-ish per person.