My question is regarding exercise 5a on page 7: https://www.math.ucdavis.edu/~soshniko/135b/Mid1Sol.pdf
I can see why the probability is $i\over6$ for the maximum to stay the same at the next throw, that is that the dice shows the same or less as the previous maximum.
But I don't understand the second part, that there is a $1\over6$ chance that the new die is bigger than the previous maximum. Shouldn't it be $1-\frac16$, or what am I misunderstanding?