In a certain village, it is traditional for the eldest son (or theolder son in a
ID: 2916888 • Letter: I
Question
In a certain village, it is traditional for the eldest son (or theolder son in a two-son family) and his wifeto be responsible for taking care of his parents as they age. Inrecent years, however, the women of this village, not wanting thatresponsibility, have not looked favorably upon marrying an eldestson.
a) If every family in the village has two children, what proportionof all sons are older sons?
b) if every family in the village has three children, whatproportion of all sons are eldest sons?
Explanation / Answer
Assuming that we are taking the proportion only over sons: a) If every family in the village has two children (sons), then half of the children are older sons and the other half younger sons. Thus, the proportion is 1/2. b) If every family instead has three children (sons), the one-third of the children are eldest sons, one-third are in the middle, and one-third are youngest. Thus, the proportion is 1/3. It is more complex if the children could be daughters. a) If every family in the village has two children, then half of the children are older and the other half younger. Assuming equal probability of a child being a boy or girl, the probability of each is 1/2. Then by the independence of events, the proportion of older sons must be 1/2*1/2=1/4. b) Analogously, 1/6 is the proportion of eldest sons.