Question

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. 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. 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. Follow the method of

Answer 1

Answer:

Let the G represent the Girl child

and, B represents the Boy child.

Then Sample Space = {BGG, GBG, GGB, BBG, BGB, GBB, BBB, GGG}

Thus, There are 8 sample space.

Then, Probability that couple have 1 boy = {BGG, GBG, GGB}

=  3 ÷ 8 = 0.375

Probability that couple have 2 boys = { BBG, BGB, GBB}

= 3 ÷ 8 = 0.375

Probability that couple have 3 boys = {GGG}

= 1 ÷ 8 = 0.125