a box contains 4 red balls and 4 black balls . one by one , every ball is selected at random without replacement . what is the probability that the fourth ball selected is black ?
"my complicated version of your simple approach let the 4 black balls be bbbband 4 red balls be rrrr they can be arranged in 8 slots _ _ _ _ _ _ _ _ in ( 8 ! ) / ( 4 ! x 4 ! ) if the fourth slot is black ball then the arrangement will be to fill _ _ _ b _ _ _ _ we have 7 slots and 3 black ( bbb ) and 4 red ( rrrr ) they can be arranged in ( 7 ! ) / ( 4 ! x 3 ! ) hence required probability = [ ( 8 ! ) / ( 4 ! x 4 ! ) ] / [ ( 7 ! ) / ( 4 ! x 3 ! ) ] = 2 e"
divide(add(4, 4), 4)