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)