Consider an atom of uranium 238. It has a constant probability of per unit time of emitting an alpha particle. Unlike people, it does not get tired and frail. The probability that it goes ping in the next second remains constant, however long it has survived already. That probability is extremely small. The half-life is more than 4 billion years, similar to the age of the earth. Whenever it happens, it was extraordinarily unlikely to happen just then. It has decayed 4 billion years ahead of its expected remaining lifetime.
But in a quarter kilogram of U238, it will happen 4 million times a second.
Consider an atom of uranium 238. It has a constant probability of per unit time of emitting an alpha particle. Unlike people, it does not get tired and frail. The probability that it goes ping in the next second remains constant, however long it has survived already. That probability is extremely small. The half-life is more than 4 billion years, similar to the age of the earth. Whenever it happens, it was extraordinarily unlikely to happen just then. It has decayed 4 billion years ahead of its expected remaining lifetime.
But in a quarter kilogram of U238, it will happen 4 million times a second.
Ok—I see the analogy. Though not sure it points to a clear solution to the paradox.