What are the percent chances of rolling a number when you roll two dice and take the higher number?

Question

Say I roll two twenty-sided dice and always take the higher number rolled, and dispose of the lower number. What are the percent chances of rolling each number on the die? I tried the equations in this question: What is the average of rolling two dice and only taking the value of the higher dice roll? But for some reason I couldn't get the correct answer.

Answer 1

There is $1$ way to get a $1$, namely $(1,1)$

There are $3$ ways to get a $2$, namely $(1,2),(2,2),(2,1)$

There are $5$ ways to get a $3$, namely $(1,3),(2,3),(3,3),(3,2),(3,1)$

In general there are $2k-1$ ways to get a $k$.

The basic percentage unit is $0.25\%$, so the percentage chance to throw a $k$ is $(\frac{2k-1}{4})\%$, e.g. for $k=5$ the percentage is $1.25\%$.