A certain couple is equally likely to have either a boy or a girl. If the family has four children, let X denote the number of girls.
a. Identify the possible values of the random variable X.
b. Determine the probability distribution of X. (Hint: There are 16 possible equally likely outcomes. One is GBBB, meaning the first born is a girl and the next three born are boys.) Use random-variable notation to represent each of the following events. Also use the special addition rule and the probability distribution obtained in part (b) to determine each event's probability.
The couple has
c. Exactly two girls.
d. At least two girls.
e. At most two girls.
f. Between one and three girls, inclusive.
g. Children all of the same gender.