So I'm looking to calculate the probability that a bacterial population dies out with the following conditions:
- Initial population is 1
- At each iteration the bacteria can die, do nothing, divide into 2 or divide into three. So each bacteria can change into either 0, 1, 2, 3 bacteria.
- Each event has a 25% likelihood.
So I know from simulation that the likelihood of the population dying out is ~36.3%. However, I'm looking for a method to calculate this analytically.
Some MATLAB code for the simulation:
ntries = 100000; mnum = 10000; res = ones(ntries, 1); for i = 1:ntries while res(i) > 0 && res(i) < mnum res(i) = sum(randi(4,res(i), 1)-1); end end mean(res==0)