This is like a common core math problem. Poorly worded to the point of obscuring any real math talent that could be applied in finding a “correct” result, and instead we get to debate what the question means.
A more interesting question, I think, is given a POW algorithm which adjusts difficultly to target a 10 minute block rate, and assuming network hash rate is constant and propagation is instant, what percentage of blocks take 20 minutes to solve? 60 minutes? And what’s the odds of solving two blocks in <= 60 seconds?
I don't think the question is poorly stated, and all of your questions miss the interesting bit of this one, which is that you are more likely to randomly select a long interval rather than a short one.
* What is the average time it takes to mine a block?
* If I choose a time uniformly what is the expected time it will take to mine that particular block.
The difference between them being that blocks that take a long time occupy more space on the timeline than shorter blocks and are therefore more likely to be chosen.
>What is the average time it takes to mine a block?
How do you get this question from CyrusL's original question? CyrusL explicitly specifies that it is 10 minutes per block [0], and that he is uniformly picking a point in time.
[0] Admittedly, he does not specify that it is a Poisson distribution.
A more interesting question, I think, is given a POW algorithm which adjusts difficultly to target a 10 minute block rate, and assuming network hash rate is constant and propagation is instant, what percentage of blocks take 20 minutes to solve? 60 minutes? And what’s the odds of solving two blocks in <= 60 seconds?