Assume:

(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?

## The Mathroom!

Posted by mathfail
on September 22, 2011

Posted by mathfail
on September 22, 2011

(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?

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 🙂

0 0