Risk of extinction of Schrödinger's cats I am interested in how uncertainty can be accounted for when considering the risk of extinction of a species. Forgive me for extending a rather tired thought experiment, but at least it's familiar territory and I hope it illustrates what I am trying to understand.
Let's say that Schrödinger was not satisfied with killing and not killing only one cat, so he went out and collected the last 15 remaining Himalayan Snow-Cats. He put each one in a box with a vial of poison, hammer, and a trigger device for releasing the hammer. Each trigger device has a known probability of releasing the hammer within any given hour, and the poison will take 5 hours to kill a cat (things got a bit trippy when he used radioactive decay, so this time he steers clear of quantum mechanics). After one hour, Schrödinger receives a notice from the ethics board telling him he's nuts and ordering him to release the cats immediately. He pushes a button which opens a cat-flap at the back of each box, thus releasing them all back into the wild. By the time the humane society check the boxes, all the cats have bolted. Before anyone can restrain him, Schrödinger detonates the remaining triggers, so nobody knows how many of the cats were poisoned.
The probability that each of the cats is poisoned is as follows:


*

*0.17

*0.46

*0.62

*0.08

*0.40

*0.76

*0.03

*0.47

*0.53

*0.32

*0.21

*0.85

*0.31

*0.38

*0.69


After 5 hours have elapsed and all poisoned cats have died, what is the probability that there are:


*

*(A) More than 10 Himalayan Snow-Cats still alive 

*(B) 10 or less still alive

*(C) 5 or less still alive

*(D) 2 or less still alive

 A: Let $p_k, k=1, \ldots, K=15$ be the survival probabilities for individual snow cats.


*

*Initialize the number of cats accounted for so far $k \leftarrow 0$, the vector of the binomial survival probabilities $(\pi_0^{(0)}, \pi_1^{(0)}, \ldots, \pi_K^{(0)}) \leftarrow (1, 0, \ldots, 0, 0)$

*While there still are unaccounted cats, $k \le K$, repeat steps 3-5:

*Increase $k \leftarrow k+1$

*Update the 0 outcome (death): $\pi_j^{(k)} \leftarrow \pi_j^{(k-1)} (1-p_k), j=0, \ldots, K$

*Update the 1 outcome (survival): $\pi_{j+1}^{(k)} \leftarrow \pi_{j+1}^{(k)} + \pi_j^{(k-1)} p_k, j=0, \ldots, K$


I would probably be paranoid about accounting for everything, and make sure that my probabilities still sum up to 1 at each iteration after step 5.
My results are:
4.091e-08  
2.647e-06  
.00006039  
.00069791  
.00479963  
.02141555  
.06519699  
.13945642  
.21276277  
.23238555  
.18045155  
.09775029  
.03565983  
.00823336  
.0010688  
.00005826  


The sum of the first three is the prob of being critically endangered, the last 5, the prob of least concern, etc.
