You have seen a number of different probability models:

• the vase model where a probability problem is equated to sampling a number of marbles of different colours from a vase;

• the binomial probability model where you are dealing with a sampling-with-replacement vase model, with precisely two possible outcomes for every sample (two "colours": "yes" or "no");

• the normal probability model where you have a continuous variable that can take any value within a specific interval (such as "height", "weight", etc.).

It is important to choose the appropriate model when confronted with a probability problem.
In order to make the correct choice, you should first look at your variable:

• if it can only take on "discrete" values, then you should think of a vase model or a probability tree;

• if it can take any value within a given interval, then you should think of a normal distribution.

Did you decide to use the vase model, but your numbers are so large that you cannot draw a useful tree? Then you should perhaps consider using a binomial distribution...

This is by no means the end of the story: there are probabiilty problems that require quite different approaches. Perhaps you will encounter these at a later stage.