Yes ames you are correct, the answer is 1/4.
Here’s how I solved the problem when I had it on an exam.
There are 1,326 unique ways to choose 2 cards from a standard 52 card deck. (52 x 51 / 2 = 1,326. We divide by two since order doesn’t matter i.e. a seven of spades and a king of clubs is the same group as a king of clubs and seven of spades.)
Of the 1,326 possibilities 78 include 2 hearts (13 * 12 / 2= 78), 507 include one heart and one non-heart ( 2 * (13 * 39 / 2) = 507) and 741 consist of two non-hearts (39 * 38 / 2 = 741). (Please note that 78 + 507 + 741 = 1,326.)
If two hearts are missing from the deck the probability of picking a heart is 11/50.
If one heart is missing from the deck the probability of picking a heart is 12/50.
If no hearts are missing from the deck the probability of picking a heart is 13/50.
So the probability of two hearts missing (78/1,326) x the probability of picking a heart (11/50) = (78/1,326)*(11/50).
Summing up the probabilities from all three scenarios gives us (78/1,326)*(11/50) + (507/1,326)*(12/50) + (741/1,326)*(13/50) = 1/4.