**SOLUTION:**

__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)**