Consider a poor couple making decisions about the number ofchildren. Suppose that in this society, there is no old ageinsurance, and parents must rely on their children for support.
Parents would like to receive old age support with a probabilityof at least q. Denote the number of children by n. Let p be theprobability that a child (male or female) looks after the parentsin old age.
a) What is the probability that a child does not look after theparents in old age?
b) What is the probability that out of n children at least onechild looks after the parents in old age? Assume each child’sdecision is independent of all others.
c) Find an expression that gives the optimal rule for theparents for deciding the number of children, given that they wantthe probability of being looked after to be at least q.
d) Let q=15/16 and p=1/2.What is the number of children thatthis couple will choose to have?
