In: Statistics and Probability
Consider a poor couple making decisions about the number of children. Suppose that in this society, there is no old age insurance, and parents must rely on their children for support.
Parents would like to receive old age support with a probability of at least q. Denote the number of children by n. Let p be the probability that a child (male or female) looks after the parents in old age.
a) What is the probability that a child does not look after the parents in old age?
b) What is the probability that out of n children at least one child looks after the parents in old age? Assume each child’s decision is independent of all others.
c) Find an expression that gives the optimal rule for the parents for deciding the number of children, given that they want the 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 that this couple will choose to have?