When reading questions like these, watch out for "or", which means to add.
There are a total of 15 tiles;
There are 5/15 (1/3 simplified) A tiles.
There are 3/15 (1/5 simplified) E tiles.
There are 1/15 Z tiles.
There are 2/15 M tiles.
There are 3/15 (1/5 simplified) L tiles.
There is 1/15 Y tiles.
We are looking for E or Y, which means we must add their fractions together.
E = 3/15, Y = 1/15.
3/15 + 1/15 = 4/15
You have a 4/15 chance of drawing an E or a Y.
I hope this helps! :)