I'm studying for CAS/SOA Exam 1/P and I'm stumped on this question. It says:

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> From the set of families with two children a *family* is selected at random. Let $X\_1=1$ if the first child of the family is a girl; $X\_2 = 1$ if the second child of the family is a girl; and $X\_3 = 1$ if the family has exactly one boy. For $i=1,2,3$ let $X\_i = 0$ in other cases. Determine if $X\_1,X\_2$, and $X\_3$ are independent. Assume that in the family the probability that a child is a girl is independent of the gender of the other children and is $\frac12$.
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I'm just really stuck with the events here and I think that's what's throwing me off. A little help?