Lets say there are 200 tickets in a lottery system. Six tickets are drawn one by one, without replacement. These six tickets win a prize. Lets say you bought 1 ticket, what is the probability that you win a prize?

The obvious answer would just be 6/200 = 3%, but isn't it more than that since the odds of winning get better every ticket draw? (1/200 for first ticket, 1/199 for second, etc...) This would make sense, but the idea fails when you use it for a scenario with 5 tickets and 4 winning draws. P(winning) would then be 1/5 + 1/4 + 1/3 + 1/2, but that value is bigger than 1.

Not sure where I'm missing something here... The problem seems so simple but I just made a mistake somewhere.