The Mathroom!

(1) 20% of all people are “black” (100%)
(2) All mating is random
(3) Once you go black, you never go back.
How long until everyone on earth is at least 50% black?

via The Weinerworks » The Mathroom!.

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  1. So basically the last white surviving must have had all white predecessors. The equation to solve is then:
    0.8^n (the probability of having 100% white predecessors) * 7*10^9 (population of the earth today) = 1 (the last white person)

    Taking the logarithm left and right gives you n= 101 generations 🙂

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