Answer to Question #152564 in Statistics and Probability for Daniel

Question

consider the composition of a 3-child family in which the children were born at different times but a girl is as likely as a boy at each birth What is the probability that the oldest child and the youngest child are of the same gender?

a. 0.25
b. 0.5
c. 0.375
d. 0.75

Answer 1

Let's denote B for the birth of the boy and G for the birth of the girl.

There 8 possible outcomes:

BBB, BBG, BGB, GBB, BGG, GBG, GGB, GGG

the oldest child and the youngest child are of the same gender: BGB, GBG

Therefore the probability that the oldest child and the youngest child are of the same gender is $\frac{2}{8}=\frac{1}{4}=0.25$

Answer: a