At time 0, a blood culture starts with one red cell. At the end of one minute, the red cell dies… 1 answer below »
At time 0, a blood culture starts with one red cell. At the end of one minute, the red cell dies and is replaced by one of the following combinations with probabilities as indicated:
Each red cell lives for one minute and gives birth to offspring in the same way as the parent cell. Each white cell lives for one minute and dies without reproducing. Assume the individual cells behave independently.
(a) At time n + ½ minutes after the culture began, what is the probability that no white cells have yet appeared?
(b) What is the probability that the entire culture dies out eventually?
