Combination of the binomial and Poisson distributions. Suppose that the probability of an insect laying r eggs is p(r; 2) and that the probability of an egg developing is p. Assuming mutual independence of the eggs, show that the probability of a total of k survivors is given by the Poisson distribution with parameter 2.p. Note: Another example for the same situation: the probability of k chromo- some breakages is p(k; 2), and the probability of a breakage healing is p. [For additional examples of a similar nature see IX, (1.d) and XII, 1.]