Maximum amount of tries to pick a red marble in a bag of 99 other black marbles (with replacement). I have a bag of 100 marbles, 99 black, 1 red. 
What is the maximum amount of tries it would take to pick the red marble assuming you place the marble back in the bag after your pick it up?
I know that the chance is 1%, so the average amount of tries in a normal distribution would be 100 to get the red marble. However you cannot be sure that you will have picked the red marble in the first 100 tries, 200 tries, etc. But as the tries increase, the probability of not having picked the red marble goes down increasingly. 
At what point would it be considered impossible not to have picked a red marble?
 A: It depends how you define "impossible". 
Colloquially speaking, you could define it to mean if the chance is less than some tiny $\epsilon$, then it is "impossible". 
Then you could solve for the number of picks that would satisfy that.
Most people would probably be unsatisfied with that though. (Even if $\epsilon=10^{-1000}$ the event could still technically happen)
In stricter sense of the word, one might ask for the probability to be $0$. 
This is not miniscule; it means literally zero.
In this case, the number of picks would have to go to infinity; in the situation described, this will never happen, because there will always be a non-zero chance of picking a string of one color, no matter how long that string is. No matter how small $0.99^n$ is (or how large $n$ is), the probability is positive.
In fact, for me personally, even zero probability is not strong enough for me to call an event "impossible". For instance, consider choosing a real number $c\in\mathbb{R}$ uniformly in the interval $[7,13]$. What is the probability of choosing exactly $c=9.713$? It is zero. But is it possible? Yes. It is a number inside the interval. To me, therefore, it is not impossible. 
Impossible is a bit of a high bar in that sense :D
A: You can never be certain to pick the red marble, of course.  At every step there are black marbles.
In fact, you can never be certain to pick a black marble either, of course.  It is possible (though unlikely) you keep picking the sole red marble.  The chance of that, over $n$ picks, is of course $0.01^n$.
A: Probability for obtaining a red marble at least one time in $n$ tries is
$1-0.99^n$
for $10$ tries, it is $0.095$
For $100$ tries, it is $0.633$
For $1000$ tries, it is $0.999$
But we cannot define maximum accurately. 
