Calculations of Dependent vs. Independent Event Trials

A box contains \(3\) balls labelled \(3\), \(6\) and \(9\). A second box contains another \(3\) balls labelled \(4\), \(6\) and \(8\). A ball is drawn at random from each box and the number is recorded.

1. Draw a tree diagram to show all the possible outcomes.
2. Find the probability that
   1. the sum of the two numbers is more than \(10\),
   2. the product of the two numbers is a perfect square.