AMC 12A 2015 Problem 24

Rational numbers a and b are chosen at random among all rational numbers in the interval [0,2) that can be written as fractions \dfrac{n}{d} where n and d are integers with 1 \leq d \leq 5. What is the probability that

(\cos (a \pi)+i \sin (b \pi))^{4}

is a real number?

Answer Choices
A. \dfrac{3}{50}
B. \dfrac{4}{25}
C. \dfrac{41}{200}
D. \dfrac{6}{25}
E. \dfrac{13}{50}