The chances of drawing a red marble are 20% when there are 15 red marbles and 75 marbles total. (If there are 14 or fewer red marbles, Orin has already quit the game.) If there are more than 75 marbles total, then the probability of drawing a red marble is less than 20%.
Since there are 100 marbles to start with, Orin can draw a maximum of 25 marbles before his probability of drawing a red marble reaches 20%.
Your number is 25.
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If Orin could keep drawing marbles after drawing a red one, he could draw all 100 marbles without the probability of drawing a red one being more than 20%. To do that, he'd have to draw the red ones first, or at regular intervals throughout (favoring sooner, rather than later).
