In a certain town, 10% of the families have no children, 10% have one child, 40% have two children, 30% have three children, and 10% have four children. Assume that births are independent of each other, and equally likely to produce male or female.
a) One family is picked at random from all of the families in this town. What is the probability that there are at least two children in the family?
b) One family is picked at random from all of the families in this town. Guess the size of the family, given that it has at least two girls. Give reasons for your guess.
c) A family is picked at random from among the families with four children. Then, a child is picked at random from the selected family. What is the chance that the child picked is a girl with at least one brother?