Bitcoin mining probabilities

A miner with hash power of 1 kilohash per second is weaker than a miner with hash power of 1 gigahash per second only on an ex ante probabilistic basis. The first miner might solve a block on his secomd attempt while the second miner might fail to do so even after hundreds of trillions of attempts.

Similarly, the sane "weak" miner might solve a block on his second attempt even when the network difficulty is astronomically high, both in absolute terms and relative to his tiny hash power.

Question: is there anything fundamental that I am missing in those two statenents and that makes these two statements false?