If you take two balls randomly out of a jar of colored balls, there is a 50% chance that the balls will both be red.

What is the total percentage of red balls in the jar?

(In reply to a mathematecally more rigorous solution by TomM)

There must be a flaw in the reasoning, as an original supply of 85 red balls out of 120 balls also produces a 1/2 probability that the first two drawn will both be red. That's an initial ratio of 85/120=.7083333... A smaller number of balls that is more than the 3 red out of 4 of the proposed solution is 15 red out of 21. (15/21)(14/20)= .5 and the original ratio is 15/21=.714285714285...

Here is a table of some values:
3 / 4 = .75
15 / 21 = .7142857
85 / 120 = .7083333
493 / 697 = .7073171
2871 / 4060 = .7071428
16731 / 23661 = .707113
97513 / 137904 = .7071078

The table was produced by solving 2r(r-1) = (r+g)(r+g-1) as a quadratic equation in r using the quadratic formula to get r = g + .5 + √(2g²+.25), and printing any r that is an integer and the denominator which is r+g.

Posted by Charlie on 2003-02-17 14:36:06