Reserve
Person A, assumes the lightbulb is broken, and therefore replaces the bulb and flicks the switch, and the light bulb turns on.
Person B, assumes that from the start the switch was not turned on, he goes over and turns the switch and the light comes on.
Here it is obvious that person A started off on the wrong foot, even knowing that one has to turn on the light switch first to see if it will work. But he missed that the first time. But being a keener, he knew to flick the switch after replacing the bulb, and satisfied with the result, believes the previous light bulb was indeed broken.
Given the order you have placed the assumptions and the tests we cannot say that the light was not first broken but can only say that Person A did not check the issue of power first before making the assumption of the light bulb itself being broken.He may still consider his
assumption valid as a possible cause of the darkness.
Since he switched the light bulb and then turned the power on we can only conclude that he failed to test the more obvious case first, that of the power supply to the bulb.
However, Person B ,who tested the power
after person A had switched light bulbs, is incorrect in his assumptions about the power being the cause unless both he and Person A first check the original light bulb to see if that bulb was indeed the cause of the darkness.
Keep on asking questions though it might be good to loosen your grip on your assumptions lest you remain in the dark.