6. (a) A couple decides to keep having children until they have both sexes. If p is the probability of having a boy, what is the expected number of children they will have? (Hint: Use the method of Example 25 on page 167 of Rosen to evaluate the summation, giving the answer .) Does your answer make sense if p 0 or p 1? Explain. (b) A different couple decides to keep having children until they have a child of the same sex as their first child. If p is the probability of having a boy, 1 > p > 0, what is the expected number of children they will have? What if p = 0 or p = 1? Explain