I may not be reading this question right, but adding the light confuses me.
I used rand in excel to check my ailing probability abilities and with 1000 numerical draws, i have individuals visiting the room between 4 and 17 times.
If I do the same thing reflecting only 300 draws, there are many zeros in my chart. If the prisoners know these things, they'd be hesitant to declare that all prisoners have visited the room. Even with some zeroes, a couple of prisoners have visited 9 times by then, so it wouldn't be safe for a prisoner who visited 7 times to say "ghee, everyone must've been here by now".
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- Late Friday Puzzler -- 100 Prisoners