Justice is Colour Blind!!
In the country of Fictopia, there are two different parties, Red and Blue. Their Supreme Court is supposed to have 11 judges, but right now it has only 2: one Red and one Blue. For each of the next 9 months, a new judge will be added, with her party randomly matching either Red or Blue, with probability proportional to the relative makeup of the Court so far.
(For example, in the first month, the new judge is equally likely to be Red or Blue, but in the second month, the probability will be 2/3 in favour of the majority party represented on the court, and so on.)
What is the probability that at the end of the process, the court has 1 Red and 10 Blue judges?
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1 solution
Working it out month by month:
2 1 ∗ 3 2 ∗ 4 3 . . . 1 0 9 = 1 0 1 = 1 0 %