The probability is 9/50.
The probability of getting a blue paper clip from the first clip is 3/10, since there are 3 blue clips out of 10 total.
The probability of getting an orange paper clip from the second cup is 6/10, since there are 6 orange clips out of 10 total.
Together, the probability is 3/10(6/10) = 18/100 = 9/50