For Halloween Jane offers the trick-or-treaters three bags to choose from, identical except one is orange, one is black and one is purple. Each bag contains two different types of candy bars. At the beginning of the night, the orange bag contains 8 chocolate bars and 4 nut bars, the black bag contains 4 chocolate bars and 10 nut bars and the purple bag contains 6 chocolate bars and 8 nut bars. The probability that a trick-or-treater will choose the purple bag is 35%, the orange bag is 35% and the black is 30%.
(a) The probability that a nut bar was chosen given that it came from the orange bag is
(b) The probability that a nut bar was chosen is
(c) The probability that the orange bag was chosen given that a nut bar was picked is
