Thought process -

I think the three balls can be drawn in 4 ways

1) All the three balls are black = 5/8 .4/7 .3/6 then the probability of next black ball can be drawn is 2/5.

2) 2 black and 1 red = 5/8 . 4/7 . 3/6 then the probability of next black ball can be drawn is 3/5.

3) 1 black and 2 red = 5/8 . 3/7 . 2/6 then the probability of next black ball can be drawn is 4/5.

4) All red = 3/8 . 2/7 . 1/6 then the probability of next black ball can be drawn is 1.

Probability = (option1 + option 2 + option3 + option 4)/chosing one out of four

= (2/5 + 3/5 + 4/5 + 1)/4C1 = 14/20 = 0.7

Please let me know if the way I am thinking is right.

Anshu.