Question

A single cell can either die, with probability .1, or split into two cells, with probability .9, producing a new generation of cells. Each cell in the new generation dies or splits into two cells independently with the same probabilities as the initial cell. Find the probability distribution for the number of cells in the next generation.

Answer 1

A single cell can die, with probability .1

So, the probability distribution for next generation, P(a cell can die) = 1/10

A single cell can split into two cells,,  with probability .9

So, the probability distribution for next generation, P(a cell can split into two cells) = 9/10