# Probability of expected size

1. Mar 17, 2009

### 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?

2. Mar 17, 2009

### needhelp83

Would this be equivalent to:

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

3. Mar 17, 2009

### leumas614

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