I think the ans is 29/50.My method is

SUM                   tot no. of numbers

0                                          1²

1                                          2²

2                                          3²

.

.so on

9                                         10²

10                                        9²

11                                        8²

so on

18                                        1²

So,the total no. of numbers are 2(1²+2²+....+9²)+10²=5800

Hence the probability is 5800/10000=29/50