let the no be abcd

the no. of ways in which the

sum(a+b) can be attained 1,2,3.......9, 9, 8,...... 1

the diff. values taken by a+b 1,2,3,.......9,10,11,......18

the no. of ways in which the 2,3,4,......10, 9 ,8,........ 1

sum(a+b) can be attained

now we can use total prob. theorm. let A - event that a+b = c+d, and e1-event that a+b =1,e1- enent that a+b=2.... e18-event that a+b=18. 

p(A) = p(A/e1).p(e1) +.........p(A/e18).p(e18)

p(e1)=p(e2)=......p(e18) = 1/18(one out of 18 possibilities)

now p(A/e1) = 2.1/9000 p(A/e2) = 3.2/9000 ......p(A/e18) = 1.1/9000 (from the above table)