jmc

This problem requires a little bit of casework. There are four ways in which the dice can both show the same thing: if they both show maroon, both show teal, both show cyan or both show sparkly. The probability of getting maroon is $\frac{4}{20}$, so the probability that they will both show maroon is ${\left(\frac{4}{20}\right)}^2=\frac{16}{400}$. Similarly, the probability of getting teal is $\frac{7}{20}$, so the probability that they will both show teal is ${\left(\frac{7}{20}\right)}^2=\frac{49}{400}$, the probability of getting cyan is $\frac{8}{20}$, so the probability that they will both show cyan is ${\left(\frac{8}{20}\right)}^2=\frac{64}{400}$ and the probability of getting sparkly is $\frac{1}{20}$, so the probability that they will both get sparkly is ${\left(\frac{1}{20}\right)}^2=\frac{1}{400}$. So our answer is $\frac{16}{400}+\frac{49}{400}+\frac{64}{400}+\frac{1}{400}=\frac{130}{400}=\boxed{\frac{13}{40}}$.