a box contains 3 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 5 black balls be bbbbb and 3 red balls be rrr they can be arranged in 8 slots _ _ _ _ _ _ _ _ in ( 7 ! ) / ( 4 ! x 3 ! ) if the fourth slot is black ball then the arrangement will be to fill _ _ _ b _ _ _ _ we have 7 slots and 3 black ( bbb ) and 3 red ( rrr ) they can be arranged in ( 6 ! ) / ( 3 ! x 3 ! ) hence required probability = [ ( 7 ! ) / ( 4 ! x 3 ! ) ] / [ ( 6 ! ) / ( 3 ! x 3 ! ) ] ans = 7 / 4 a
divide(add(3, 4), const_4)