(1) A family has three children.  Assume that each child has an equal probability of being a
boy or a girl.  Also assume that the genders of the individual children are independent.  
Find the probability  P[X and Y], where X is the event that the oldest child is a girl, and
Y is the event that, among the three children, there are exactly two girls.  

(2) A population consists of people of three different types:  A, B, and C.  There are twice as
many Type A people as Type B people, and twice as many Type B people as Type C
people.  The probability of having a claim during a given year is 0.50 for Type A people,
0.30 for Type B people, and 0.10 for Type C people.  Each person will either have a
claim, or have no claim.  An insurer picks a person at random from the population, and
observes that, after one year, this person had no claim.  Find the probability that this is a
Type C person.

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