Consider a bucket full of cheese and caramel popcorn. You pull out two random pieces of popcorn at a time to eat. You record the number of cheese-cheese, cheese-caramel, and caramel-caramel pairs that you eat (as you do when eating cheese and caramel popcorn). You find that you ate 50 cheese-cheese pairs, 40 cheese-caramel pairs, and 10 caramel-caramel pairs. Calculate the proportion of the bucket that was made up of caramel popcorn.