With probability XX + Y, we select the bottom card of the first pile and put the selected card to the top of the new pile. Then, with probability YX + Y, we select the bottom card of the second pile and then put the selected card to the top of the new pile.

밑줄 친 부분이 원래는 분모가 X+Y이고 분자가 각각 X와 Y인 수식으로 나타나야 합니다.