Could anyone help me?A bacteria has 1/3 probability to die and 2/3 probability to divide into 2 identical cells.What is the probability that all the bacteria die ?That is: finally, there is no bacteria anymore.
Are you looking for the prob that all will all die over an n generations or just after the first generation?
If there are P bacteria in the initial (0th generation) population then the prob they all die after the 0th generation is
(1/3)(1/3)(1/3)(1/3) ...(1/3) with P factors.
It gets more complicated if you want to extend to n generations.