Originally Posted by

**undefined** Oh, we posted at almost the same time, haha.

Yes, the second generation probability I gave is p(B|A) where A = the first reproduction was successful, and B = the race goes extinct at that generation.

For the 3rd generation, we consider cases.

Case 1: John was successful, and both of his two children were successful. So there are 4 bacteria, and the probability of extinction right now is (1/4)^4 times the probability of getting to this state, or (3/4)(3/4)(3/4).

Case 2: John was successful, and Child A failed, but Child B succeeded. There are two bacteria now, so we have (1/4)^2 times the probability of getting there, (3/4)(1/4)(3/4).

Case 3: Same as case 2 but with Child A and Child B reversed.