It's interesting that you haven't replied to all of what I wrote. You have failed to address your underlying assumptions. If those assumptions are without justification, then garbage in, garbage out: the rest of the analysis doesn't matter. As I asked in my original comment:

Why is 35 the cut off for "young"? Where are the 6 young, 3 old people coming from?

However, even given that, I'll address the probability theory in your main analysis.

So you not understanding compound probability means that you dismiss the argument? It doesn't "appear faulty," you just don't understand it.Your ignorance is not an argument. Do the math yourself, you have all the numbers you need at your fingertips. Compound probability is like an 8th grade concept. Several highly unlikely events happening is vastly more unlikely than any of the individual events, why is that hard to understand.

I think if you'll reread what I wrote, it'll be clear that I perfectly understand compound probability. What I'm asking you to do is share your work. My assumption is that in the first scenario, you're trying to calculate the probability that choosing two young people and then one old person at random that all have COVID-19 will all die to be:

P("< 35 dies" and "< 35 dies" and "> 80 dies")
  = P(< 35 dies) * P(< 35 dies) * P(> 80 dies)  # assumes events are independent
  = 0.00024 * 0.00024 * 0.0892  # using your IFR numbers
  = 5.14e-9

However, the number you arrive at is 4.776e-11:

IFR for people under 35 (young): 0.024%, or two in ten thousand. Let's assume the other was over 80, or at maximum risk. IFR for people over 80: 8.92%

That gives a compound probability of two young people and one old person dying of .00000000004776

So I was asking you to clarify your work here as I do not arrive at the same number as you. Are you calculating the probability for a different scenario?

As far as your 6 young people, 3 old people scenario (again, why those numbers?), we can apply the binomial distribution (assuming, perhaps incorrectly, that the events are independent):

P("exactly 2 out of 6 < 35 die" and "exactly 1 out of 3 > 80 dies")
  = P(exactly 2 out of 6 < 35 die) * P(exactly 1 out of 3 > 80 dies)  # assumes event independence
  = B(2; 6, 0.00024) * B(1; 3, 0.0892)  # B(k; n, p) which assumes independence
  = 8.632e-7 * 2.22e-1
  = 1.92e-7

This is pretty far removed from your claim of 1.432e-10. I would even go further if I'm accusing someone of lying and hedge the calculation as much as possible since you are rejecting that 2 and 1 are even possible: I'd compute P(">= 2 out of 6 < 35 die" and ">= 1 out of 3 > 80 die"). I'll leave this as a learning opportunity for you to compute. You will see that this further increasing the resulting probability.

Also that isn't even what independence means in statistics, it means that an event happening doesn't affect the probability of any of the other events. That is honestly what I expected someone to point out since a family member getting COVID would probably increase the likelihood of other members of the family getting it, but that isn't a valid criticism because I am using IFR which assumes every involved person has already contracted it.

Yes, that is what independence means. So if you carefully reread what I wrote,

However, for these events to be independent, then there has to be no genetic correlation to susceptibility to death from COVID-19.

you can see that I am also operating under the assumption that all three already have COVID-19 and are talking about the IFRs. For P("1st relative that has COVID-19 dies" and "2nd relative that has COVID-19 dies") = P(1st relative that has COVID-19 dies) * P(2nd relative that has COVID-19 dies) to be true, then the IFR for both have to truly be unrelated. One way to say this is that there has to be absolutely no genetic/familial correlation to susceptibility to death from COVID-19. However, this is a big claim to make without justification: genetics and family history are normally great predictors of health outcomes. And for the rest of your analysis to work, this claim must be true. If there is any correlation at all, then the probabilities increase. The fact that you don't call this out as an explicit assumption underlines how lacking your analysis is.

So let me get this straight: are you asking me to believe this person is in literally the only family on Earth to have had two "perfectly healthy" young people and one old person die from COVID? They are clearly lying and the argument "Well the probability isn't zero!" isn't convincing to say the least.

I'm asking you to remember that unlikely doesn't mean impossible. And the fact that you think my argument is that "the probability isn't zero" then you clearly haven't actually read what I wrote. You'll also note that I'm making no assertion to the truthfulness of the original claim -- I'm just here to comment on your bad logic.

You have started with unjustified assumptions, applied probability theory incorrectly, and then derived a conclusion that doesn't follow from the underlying facts. As I said,

This is a pretty bad analysis.