This is a question from the area of Probability.
If we rephrase it, you are asked the probability for obtaining an even sum from numbers 1-20.
An even sum can be obtained in two cases
(1) Sum of two odd numbers (ex.3+5 = 8 ; 7+5=12 ; 9+13=22) OR
(OR is equivalent to addition)
(2) Sum of two even numbers (ex. 4+6=10,8+10=18;12+14=26)
Thus, Probability (Even Sum)
= Prob (1st card is odd AND 2nd card is odd) OR Prob(1st card is even AND 2nd card is even)
= 10/20 x 9/19 + 10/20 x 9/19
(As cards are picked simultaneously without replacement, the sample space changes from 20 to 19)
= 1/2 x 9/19 + 1/2 x 9/19
= 9/38 + 9/38
= 18/38 (OPTION D)