7. Among the families with two children in a large city, the probability that the elder child is a boy is \(\frac { 5 } { 12 }\) and the probability that the younger child is a boy is \(\frac { 9 } { 16 }\). The probability that the younger child is a girl, given that the elder child is a girl, is \(\frac { 1 } { 4 }\).
One of the families is chosen at random. Using a tree diagram, or otherwise,

1. show that the probability that both children are boys is \(\frac { 1 } { 8 }\). Find the probability that
2. one child is a boy and the other is a girl,
3. one child is a boy given that the other is a girl. If three of the families are chosen at random,
4. find the probability that exactly two of the families have two boys.
5. State an assumption that you have made in answering part (d).