Expected Size of One-Boy Family and Probability of Girls

[needhelp83]

X is the number of girls in a one-boy family, and so X+1=the size of a one-boy family. What is the expected size of a one-boy family in terms of \alpha? What is the expected size of a one-boy family if \alpha=0.51?

\alpha=the probability that a random birth is a boy

I know this isn't difficult, but the terminology has completely gotten me confused. How do I solve for this with an actual formula?

 

[needhelp83]

Would this be equivalent to:

E[X]=\alpha + (1- \alpha) \times x

 

[leumas614]

What is a one-boy family? How can there be girls in a one-boy family?