Question

Family planning. A couple wants to have three children. Assume that the probabilities of a newborn being male or being female are the same and that the gender of one child does not influence the gender of another child.

1. There are eight possible arrangements of girls and boys. What is the sample space for having three children (gender of the first, second, and third child)? All eight arrangements are (approximately) equally likely.
2. The future parents are wondering how many boys they might get if they have three children. Give a probability model (sample space and probabilities of outcomes) for the number of boys.

Answer 1

Let B denote a boy and G denote a girl

Sample space, S = {BBB, BBG, BGB, GBB, GBG, GGB, BGG, GGG}

Let X denote the number of boys

Probability distribution table:

X	0	1	2	3
Outcomes	GGG	GBG, GGB, BGG	BBG, BGB, GBB	BBB
P(X)	1/8	3/8	3/8	1/8