Probability to win a chance game The game is quite simple, let's put it in marbles terms :
There's a bag of 25 marbles, 1 is white.
Each user picks one, and doesn't put it back.
I've figured the probability of each pick to be the winning pick, but I'm struggling to figure the probability of a game to be won after N clicks. My math lessons are very far away...
So :
Pick 1 : 4% chance to pick the white marble
Pick 2 : 4.17%
...
Pick 24 : 50% chance to pick the white marble.
What's the probability of the game being won after 10 picks?
I know I can't just add all the probas I've calculated, but I'm running out of ideas and don't have the vocabulary to ask google properly.

Taking win to be drawing the white ball,
if you are asking for P(win on 10th pick), it is simply $\dfrac1{25}$,
because colors have no preference for positions.
If you are asking for P(win after 10th pick)= 1 - P(win in first 10 picks),
and since winning on any pick has the same probability, 
$Pr = 1 - \dfrac{10}{25} = \dfrac35$
