Sorry to have another Admin weighing in but probability arguments are something of an interest of mine.
Yes, you are going to have to provide your calculations. And you are also going to have to specify exactly what you are calculating ht probability
of - clearly and precisely. There are two very good reasons for this.
Firstly it is needed to check that the calculations are not only mathematically correct - but that they are the right calculations.
Secondly it allows us to determine if your probability is actually interesting. It is easy to find sequences of events with low probabilities. It would be surprising if it were not true ! Your "rule" does not apply to long series of events at all. If it did, the big lotteries would be impossible ! (Assume that each draw has the high probability of 10^-6. A sequence of 10 draws would then have a probability of 10^-60. But the big lotteries go on and on despite that "impossibility").
So this is the point. Nobody is going to argue on the basis that your numbers are right. What they are going to try to show is that your numbers are wrong or of no real significance. And to argue that we are going to have to see how you got those numbers and what they really mean. That is absolutely essential to any worthwhile discussion of this topic.