You cannot precalculate when an event may happen like this, that would violate you having a constant chance of finding a hash, and would make it dependent on the past.
Thank you for the detailed, thorough response. Give me a chance to digest everything you said. You are clearly more advanced in mathematics and statistics than I (i mean that genuinely not sarcastically) and I would love to learn from you. However, in the mean time, let me ask you this.
If you can't precalculate (you say precalculate, I say predict) the time is takes to solve a block, how is bitcoin (or whatever coin) doing it? Bitcoin itself has to predict the time it will take the network to solve a block, to know how to adjust the difficulty. It MUST maintain an average block find time of 10 minutes, or quite literally the entire thing will come crashing to a screeching halt.
If bitcoin couldn't accurately predict the time it takes to solve a block given X hashpower, we wouldn't be having this conversation because bitcoin would have died, and none of the alt coins that we love to mine at middlecoin would have ever existed.