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Probability of selecting two blue discs back to back

Question

If a box contains twenty-one coloured discs, composed of fifteen blue discs and six red discs, and two discs were taken at random, it can be seen that the probability of taking two blue discs, P(BB) = (15/21)×(14/20) = 1/2.

The next such arrangement, for which there is exactly 50% chance of taking two blue discs at random, is a box containing eighty-five blue discs and thirty-five red discs.

By finding the first arrangement to contain over 1012 = 1,000,000,000,000 discs in total, determine the number of blue discs that the box would contain.

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Spoiler

59aae63fa8a2f_bluereddiscs.jpg.6c881e799203486c3d8c1f39958716fb.jpg

The picture in the spoiler above is an explanation with formulas that wouldn't look very nice if I tried to just write them out in text.

Edited by plasmid
changed to solve for the number of blue discs instead of the total number of discs

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