Does probability of $1$% means that it is guaranteed to get a success event if I do $100$ tries? Let us suppose I have $100$ balls in a container, each one has a different number ( from $1$ to $100$).
I want to pick a ball, and we'll suppose this is a random process ( i.e. choosing the ball is random).
Question $1$
Given that the whole universe of balls ( a.k.a the set Ω) is made up of only those $100$ balls in the container, I can say that probability of picking up the ball i is 1% (i is any number from $1$ to $100$)?
Question $2$
If the answer to question $1$ is "yes", and if I repeat the picking of a ball $100$ times (each time I put it back in the container, and I will suppose that the next pickup is unrelated to the previous one, hence randomness), Is it guaranteed that the ball i will appear at least one time during the $100$ pickups?
Note: I am not a total beginner in maths, but I am confused about something: does a n% chance means that it is guaranteed to get n successes out of $100$ tries, or it is not guaranteed unless I repeat the tries till infinity?
 A: An $n$% chance means that, if you try a very large number of times, the fraction of successes will be approximately $n/100$. Additionally, as you do more and more tries, the difference between the measured fraction and $n/100$ will tend to get smaller and smaller.
However, while the probability of getting zero successes gets smaller and smaller as the number of tries $N$ goes up, it is never zero. That probability is given by the simple formula
$$
P(\mathrm{no\;success}) = \left(1 - \frac{n}{100}\right)^N
$$
And finally, an important point. This probability applies to a set of $N$ trials taken as a whole. The probability of success for any individual trial is still $n/100$, no matter how many successes or failures occurred before it. If you draw from the container 10000 times and never draw ball 15, then you've been astonishingly unlucky, but on the next draw, ball 15 still has a 1% chance of being chosen.
A: Reduce the number of outcomes from 100 to 2 and you have this question: If you flip a fair coin twice, are you guaranteed to get one head and one tail?  This one you can verify experimentally as well as analytically.
Like Ted says in the comments, there are no certainties in probability.  There's also no such thing as "infinitely many trials."
The best we can do is say something like the law of large numbers:
If you draw one ball from the 100 $n$ times, and keep a running total of the fraction of the times that ball $i$ is drawn, this fraction converges in probability to $0.01$ as $n$ becomes arbitrarily large.
A: As a student and teacher of maths, I'm going to approach this pretty informally.
Measuring probability, in the case of finite sample spaces, is a ratio of favorable outcomes to total outcomes. So, if you have 100 balls numbered 1 to 100, the probability of selecting ball 1 is, well, 1 in 100. There is one outcome you desire of the hundred available.
This does not mean, however, that if you draw 100 balls with replacement, you are gauranteed to select ball 1 once. You could possibly never draw it!
