Chapter 5.4, Problem 17E

In a study concerning a new treatment of a certain disease, two groups of 25 participants in each were followed for live years. Those in one group took the old treatment and those in the other took the new treatment. The theoretical dropout rate for an individual was 50% in both groups over that 5-year period. Let X be the number that dropped out in the first group and Y the number in the second group. Assuming independence where needed, give the sum that equals the probability that $Y\ge X+2$.

HINT What is the distribution of $Y-X+25$?