By revisiting two famous questions concerning the Copenhagen interpretation of quantum mechanics, this article presents a concise analysis of the quantum measurement problems with measuring both microscopic and macroscopic objects. The method used here is mainly based on the concept ``isolated point'' in ``point-set topology''. The findings reported are as follows. (a) Einstein's argument has been misunderstood; he was opposed to the so-called ``inherently probabilistic nature'' attached by the Copenhagen interpretation to quantum mechanics rather than to the use of probability in quantum mechanics. (b) Probability used in Einstein's ensemble interpretation is identical to the quantum-mechanically calculated probability. (c) The wave-functions in Einstein's ensemble interpretation neither describe any single quantum object purportedly possessing mutually exclusive properties simultaneously when nobody looks nor collapse abruptly when an observer performs a measurement.