Tricky probability question. Competent mathematicians required!?

A)The answer's simple. Its 1/9. B)The total no. Of ways=9*9=81. The no. Of ways both nos. Equal=9 ways because you both may choose 1,1 or 2,2 etc which has totally 9 possiblites. Therefore the probability=9/81=1/9. Your guess's correct. Both are same.