AMC 10 2021b Problem 18

A fair $6$-sided die is repeatedly rolled until an odd number appears. What is the probability that every even number appears at least once before the first occurrence of an odd number? $\textbf{(A)} ~\frac{1}{120} \textbf{(B)} ~\frac{1}{32} \textbf{(C)} ~\frac{1}{20} \textbf{(D)} ~\frac{3}{20} \textbf{(E)} ~\frac{1}{6}$