Random variables Math problem

Hello, I have some trouble understanding this math problem. I will provide a couple images to explain my confusion. My notes are in red handwriting on the images.

The problem:

The hints:

Why not like this?

I hope this illustrates my confusion sufficiently.

In short: I feel like I’m calculating a difference of 30 instead of 15, when I follow the instructions from the hints. Can you please enlighten me!

Thanks for any help :)

Best regards,
Trym