Does events with $0$ probability never occur$?$ Suppose $\mathbb{N}$ as a set of all natural numbers. What is the probability that I will randomly select $2$ from this set$?$ The probability will give $0$ as answer because $\frac{1}{\infty}=0$. But we see that we can actually select $2$ so the probability cannot be $0$.
Consider a dartboard of unit area, and stipulate that a given dart will land at some “random” location on the board, with a uniform probability density distribution. The integral of the distribution over the board is $1,$ and the probability of landing within some small region of the board is proportional to the area of the region. As the size of the region goes to $0,$ the probability of landing within that region goes to $0$. In the limit, the probability of the (center of the) dart landing on any specific point is $0$. Hence, if events with probability $0$ never occur, one might think that the dart could not land in any specific place, contradicting the fact that it lands someplace with probability $1.$
Does this mean that $0$ probability doesn't mean that the event won't happen$?$
Consider a dice. What is the probability that a number greater than $6$ will come on rolling it$?$ Answer is $0$ as that event can never occur.
In both cases $0$ probability means different$?$ Why is this happening$?$ Can anyone please explain me the reasoning behid this$?$
