One evening the hutch in the garden contains 20 pregnant rabbits. The hutch is insecure and each rabbit has chance of 1/2 of escaping overnight. The next morning each remaining rabbit gives birth to a litter, each mother having a random number of offspring with the Poisson distribution, parameter 3 (this is a very unlikely tale). Assuming as much independence as necessary, determine the probability generating function of the total number of offspring. Recall that if Z - Poisson(2), then Gz(s) e/(0-1) and if 2 - Binomial(n, P), then Gr(s) = (2+ps)".