Q. 95.0( 6 Votes )

A couple has two

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


(i) Let A be the event that both children are males, then


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


So the probability that both children are males is



Let B be the event that at least one of the children is male


Then B = {(b, b), (b, g), (g, b)}, n(B) = 3


And the corresponding probability becomes



The sample space for the at least male and both being male will become


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


And the corresponding probability becomes



So the conditional probability that both are males given that the at least one is male is



(ii) Let P be the event that both children are females, then


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


So the probability that both children are females is



Let Q be the event that the elder child is a female


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


And the corresponding probability becomes



The sample space for the elder child being female and both child being female will become


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


And the corresponding probability becomes



So the conditional probability that if the elder child is female then both children are females 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
caricature
view all courses
RELATED QUESTIONS :

State True or FalMathematics - Exemplar

Fill in theMathematics - Exemplar

A speaks truth inMathematics - Board Papers

Often it is takenMathematics - Board Papers

Assume that each Mathematics - Board Papers

A bag X contains Mathematics - Board Papers