TITLE: Very probable event occuring at least once during $n$ trials
QUESTION [5 upvotes]: Assume that Bob carries eggs from point $A$ to $B$. He can carry $1$ egg each time. Let the probability that Bob breaks an egg be $0.99999$ which is almost a certain event (for me). If Bob carries $100$ eggs separately, can we say the probability of Bob breaking an egg is $0.99999 \% = 0.00999$?
I am asking because $0.99999$ is a very high probability in my opinion, and changing the try count doesn't have any practical effect on the above example.

REPLY [2 votes]: Just to make one more observation about "almost impossible events".  Consider the experiment of picking a random real number in the interval I := [0, 1) (say, but it's not really important, using an uniform random distribution) and the question "How probable is it that the picked number is rational"?
The set of non-rational numbers in I is uncountable, whereas the set of rational numbers in the same interval is countable.  It means that the probability of picking a non-rational number is infinitely larger than that of picking a rational number and, consequently, the probability of picking a rational number is 0.  However, nothing prevents you from picking 0.5, which is a perfectly possible result of your experiment.
As Dror points out, some events can have probability 0 and this does not mean that there is no possibility for them to occur.

What is the probability of an almost impossible event?

Mathematically speaking, it is 0.
"Almost" has a well-defined mathematical meaning.  A function can be almost everywhere continuous, meaning that it is continuous everywhere but in a countable set of places.  The Dirac Delta function is almost everywhere zero.
EDIT:
no, the explanation of "almost everywhere continuous" is not the one given in the last paragraph.  The truth is more complex than this, and the linked Wikipedia article gives a correct explanation.