IMO 5/8 is the answer.
All we need to know is to find the probability of seelcting the fourth ball as black.
Now there could be following 4 situations
1) 3C1*5C2( I select 1 ball fm yellow and 2 from black) .. Probability of fourth black now becomes 3/5 ..(As 3 black remains out of remaining 5 total balls)
2) 3C2*5C1( I select 2 balls fm yellow and 1 from black) .. Probability of fourth black now becomes 4/5 ..(As 4 black remains out of remaining 5 total balls)
3) 3C3( I select 3 balls fm yellow ) .. Probability of fourth black now becomes 5/5 ..(As 5 black remains out of remaining 5 total balls)
4) 5C3( I select 3 balls fm black ) .. Probability of fourth black now becomes 2/5 ..(As 2 black remains out of remaining 5 total balls)
Now lets find the probability of each above sitaution to occur.
Situation (1) can occur in 30 ways out of 56 possible ways ( 8C3 = 56) so probability = 30/56
Similary for situation(2) ,its 15/56
For situation (3), its 1/56
For situation (4) , its 10/56
Now lets combine all situations and get total probability of getting fourth ball as balck.
==> (30/56)*(3/5) + (15/56)*(4/5) + (1/56) *(1) + (10/56)*(2/5)
===35/56 => 5/8 ..So 5/8 is answer
