Actually, worst case scenario would be not drawing a red marble before the heat death of the universe, but that would be extraodinarily improbable. Actually, with 50 blue and 50 red marbles, the average number of draws to get a red marble is just 2. In fact, the probability of 10 or more draws without finding a red marble is less than 0.001. When the ratio of blue to red is 90:10, the average number of draws to pull a red is only 10 (and the probability of more than 50 draws without a red is around .005).