Imagine that you have a bag containing 10 marbles of different colors. you have drawn a marble, recorded its color, and replaced it fifty times, with the following results: 9 purple, 16 orange, 6 yellow, and 19 green marbles. make a prediction for how many marbles of each color are in the bag. show all of your work or explain your reasoning.

Set $r$ is a set of rectangles such that (1) only the grid points shown here are used as vertices, (2) all sides are vertical or horizontal and (3) no two rectangles in the set are congruent. if $r$ contains the maximum possible number of rectangles given these conditions, what fraction of the rectangles in set $r$ are squares? express your answer as a common fraction.