Two boxes, X X\,X and YYY, contain red, blue, and green pens. Box X X\,X contains 2 red pens, 5 blue pens, and 3 green pens. Box Y Y\,Y contains 6 red pens, 2 blue pens, and 2 green pens. Casey picks one pen at random from Box X X\,X and places it into Box YYY. Casey then picks one pen at random from Box YYY.
Draw a tree diagram to represent this information.
Find the probability that Casey picks two pens of the same colour.
Given that both pens are the same colour, find the probability they are both blue.
