There are 2 possibilites :
Case 1 : Lost ball is red :
In that case probability that both balls are red = 9/24 * 8/23 = 3 / 23 [Assuming we are drawing balls without replacement]
Case 2 : Lost ball is blue :
In that case probability that both balls are red = 10/24 * 9/23 = 15/92
So P(lost ball is blue) : Case 2 / (Case 1 + Case 2)
= 15/92 ( 12/92 + 15/92)
= 15/27
= 5/9 = 0.556(correct to 3 decimal places)
Hence D) should be the correct answer..