>>12156146You have not gotten the point. Everything is deterministic but probability is actually the science of uncertainty.
Let me give you an example of a problem that I've directly worked in. Suppose that you give out loans and you lose money when people don't pay them (they default). Therefore you really care about understanding how many of your clients will end up defaulting. Let's consider a few cases:
>Case 1: Your client is one day away from defaulting, and you have perfect information.In this case, if your client does not pay you by tomorrow he defaults. You also have complete information about how much money he has right now and how he plans to spend that money today. Given this, you need no probability. You simply look at the data and determine if he is planning to pay you or not. And if he doesn't even have the money then you know he won't be able to.
>Case 2: You have perfect information right now, but your client still has a month before he defaultsNow you have uncertainty. Even if you know all about your client now, who's to say that in 30 days he won't get a friend to loan him some money to pay you. Or, on the flip side, that he will squander the little money he has gambling and then won't pay you shit. Then you can't know for sure! But for many practical reasons, you may want to estimate how much money you could lose the next month. You could do it by taking all of your clients in this situation (1 month away from default) and estimating their probability to default based on that perfect information you have. Let's say that 100 loans are at risk, and the probability is 5% so you estimate 5 loans will end up in default. If you estimated well then in 30 days you will find that indeed only 4-6 people defaulted on their loans so your estimation was good. That means that in the future you could make decisions in advance
>Case 3: Your clients could be years away from default, and you do not have perfect informationWelcome to the real world.
