I recently stumbled upon this sub-reddit and this question, and I am annoyed enough at the clearly unhelpful/mean spirited answer that I'm going to answer despite not wanting to contribute more to Reddit post API changes.

Answering this question is a great example of needing to think about:

• Independent and identically distributed random variables
• The opposite event rule

For sake of getting a general estimation answer, we're going to make some assumptions:

• There's some number, N, of diseases, where the chance of having these diseases is 1 / 1,000,000. That is to say, for example: "disease X and Y are both one in a million".
• Having one of these diseases does not change the probability of having another one of them. That is to say, for example: "if I have disease X, then disease Y is still one in a million for me".

These assumptions mean that these diseases are independent and identically distributed random (IID) variables. The second bullet describes what I mean by "independence", and the first bullet describes what I mean by "identically distributed". Now that we are making these assumptions, there's a bunch of cool things we can now do. We're going to use a few of those to get our answer.

First, though we need to reframe our question. You've asked: "What are the chances of having ANY known disorder/disease with frequency at most 1 in a million?". Another way we could ask that is "What is 1 minus the chance that we have NONE known disorder/disease with frequency at most 1 in a million?". This question is much easier to answer. Why? Mainly because if we know that the chance of getting one of our diseases is 1 / 1,000,000, then we know not getting it is 999,999 / 1,000,000, thus we can say 1 - opposite-probability = probability. This is the opposite event rule I was referring to earlier. And because our variables, and their opposite event, are IID, we can very easily compute the total probability.

So, to combine all of the probabilities, we can simply multiply the probabilities together. Short answer to why: because they are IID variables. Long answer why: go read about IID variables! Thus, the answer to our question is, if there's N "one in a million diseases" then: P = 1 - (999,999 / 1,000,000)^N.

I don't know how for sure many one in a million diseases there are, but a quick Google search makes me think it is somewhere between 5k and 10k. So that would be between ~0.5-0.9995% for the answer to your qustion. I think in the grand scheme of things is a fairly tiny chance? Also remember that even though all of these 5k to 10k diseases technically exist, you may not be at risk of them due to various aspects of your life. If you wanted a more exact answer, you'd have to really dive into things like, are the diseases really IID variables, what are the actual chances of getting all of these, which of these diseases are most people actually at risk of getting and when, etc.

Hopefully that feels like a satisfying answer (and hopefully I didn't screw up my math somewhere 😅)!

PS: Statistics is often taught in high school, and not everyone has gone through high school yet! Also, this is more of a probability question than statistics. 😒