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Simple perobability question In a two child family, one child is boy.what is the probability that the other child is girl? my ans is 2/3 but the given answer is ¾ plaese show the whole process

Simple perobability question 
In a two child family, one child is boy.what is the probability that the other child is girl?
 
my ans is 2/3 but the given answer is ¾ 
plaese show the whole process
 

Grade:11

1 Answers

Utkarsh Shukla
38 Points
9 years ago
Let B---> Event that child is a boy
      G---> Event that child is a girl
In two child family, the sample space is:
{BB, BG, GB, GG}
BG and GB are listed separately because BG represents a family in which the oldest child is a boy, while GB represents a family in which the oldest child is a girl. Each of the above combinations is equally likely. Since we're told that one child (we don't know which) is a boy, we can eliminate the GG combination. Thus, our remaining possible combinations are:
S={BB, GB, BG}
Where S is the new sample space(total no. Of outcomes)
F={GB,BG}
Where F is the set of favourable outcomes.
Reqd probability= n(F)/n(S)
                          = 2/3
According to me, your answer is correct(there may be some misprint in the material provided to you).
If they could have asked the probability that atleast one child is a girl of there are two children in a family,then your answer could have been 3/4.
 

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