Q. 2 A4.3( 4 Votes )

Assume that each child born is equally likely to be a boy or a girl. If a family has two children, what is the conditional probability that both are girls given that

the youngest is a girl,

Answer :

Let b and g represents the boy and the girl child respectively.


Now if a family has two children, the sample space will be


S = {(b, b), (b, g), (g, b), (g, g)}, n(S)=4


Let A be the event that both children are girls, the


A= {(g, g)}, n(A)=1


So the probability that both children are girls is



If the youngest is a girl


Let B be the event that the youngest child is a girl


Then B = {(b, g), (g, g)}, n(B) = 2


And the corresponding probability becomes



The sample space for the both girls is girl child and the youngest is a girl will become


(AB) = {(g, g)}, n(AB)=1


And the corresponding probability becomes



So the conditional probability that both are girls given that the youngest is a girl is



Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses
RELATED QUESTIONS :