Boy or Girl

In a two-child family, one child is a boy. What is the probability that the other child is a girl?

What if the older child is a boy? Does this information change the probability that the second child is a girl?


  1. if one child is b,then there could be two possibilities- other child is boy or the other child is a girl as:
    BG or BB , the prob. that the other child is a girl is 1 case out of the 2 cases , hence prob. of other child 2 be a girl is 1/2, irrespective of the other child being a girl or boy.

  2. Total sample space BB,GB,GG,BG
    Since one child is a boy sample space is BB,GB,BG
    P(other child is girl)={GB,BG}/{BB,GB,BG}=2/3

    for 2nd part
    Sample space={BB,BG}
    Prob =1/2

  3. @ankit for first part it is written that one of them is a boy so probability will be 1/2...

  4. @priyaranjan.... its same as saying
    P(one child is girl|one child is boy)=p(onechild is boy and one child is girl)/p(one child is boy);
    (bayes theorm)
    so numerator={BG,GB}
    so ans is 2/3

    PS: here both the events are not independent so probability wouldnot be 1/2

  5. @ankit please cehck bayes theorem that you have applied..


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