SOLUTION: A family tree has three children. What is the probability that the family has 2 boys and a girl given the middle child is a boy?

You are given this configuration for children


    X    B   Y


where X and Y stand for unknown gender and B stands for boy (which is the middle child)


Here X and Y may have 2 values X= B or G, and  Y = B or G, so there are 4 possible configurations with "B" in the center.


It is your "sample space" in this problem.


You are also given that the family has 2 boys.


It means, that only these two configurations suits for the condition


    B   B   G
or
    G   B   B.


So, there are 2 favorable configurations.


The probability under the question is the ratio "favorable/total", which in this case takes the form   = .   ANSWER