A box contains 3 red balls and 3 black balls. One by one, every ball is selected at random without replacement. What is the probability that the fourth ball selected is black?  Select the correct option.
A) 1 / 4  B) 1 / 2  C) 1 / 2  D) 2  E) 2 / 3

Rationale: "my complicated version of your simple approach let the 3 black balls be bbb and 3 red balls be rrr they can be arranged in 8 slots _ _ _ _ _ _ _ _ in ( 6 ! ) / ( 3 ! x 3 ! ) if the fourth slot is black ball then the arrangement will be to fill _ _ _ b _ _ _ _ we have 5 slots and 2 black ( bb ) and 3 red ( rrr ) they can be arranged in ( 5 ! ) / ( 2 ! x 3 ! ) hence required probability = [ ( 6 ! ) / ( 3 ! x 3 ! ) ] / [ ( 5 ! ) / ( 2 ! x 3 ! ) ] = 2 d"
Answer: D