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## Homework Statement

A strand of length L begins life as all A's. Assume that each letter evolves independent of all the rest until today, 1000 generations later. Within each generation there is a ##\mu## probability that the letter mutates to either C, G, T. Finally, assume that once a letter mutates that it cannot mutate again.

Calculate the number of A's as a function of ##\mu##. Then equate this expectation to ##N_A## and write down a function for ##\mu## in terms of##N_A##.

## Homework Equations

## The Attempt at a Solution

So, I have 1000 generations where each A has the possibility to mutate to something else with probability ##\mu##. The first generation the total number of A's is ##N_A=L##. The second generation we must multiply each A by the mutation probability. Since there is L A's we will get: ##N_A=\mu L##. The third generation occurs and we have to multiply the current number of A's by ##\mu## again. Which gives us ##N_A=\mu \mu L##. Taking this to 1000 generations we'd have ##N_A= \mu^{1000-1} L## which doesn't really seem likely at all.

Any suggestions, or is this correct?