there are 100 numbers he can roll, ten are dubs
00
11
22
33
44
55
66
77
88
99
So out of 100 numbers he has ten chances, so it is 10/100, but you can reduce, so it is indeed 1/10.
its actually more than 10/100 chance. i'm not sure exactly what it is, but the probability of the second digit being the same as the first is a lot more slim than that