At the party, belinda is craving gummy bears. it so happens that the entrepreneurial soham is also at the party, selling gummy bears one by one. he has a bag of sugar-free and a bag of regular gummy bears, each containing 7 different colors of gummy bears: red, blue, green, yellow, orange, purple, and pink. when someone wants to purchase a gummy bear, soham chooses a bag uniformly at random and then pulls a piece out of that bag uniformly at random. assume that soham has an equal number of each color of gummy bear in each bag, such that he is equally likely to pick a gummy bear of each type (sugar-free vs regular) and color pair, (i. e. it is equally probable that the soham will pull out a sugar-free, red gummy bear as a regular, purple gummy bear). further assume that each time soham sells a gummy bear, he immediately replenishes the bag he took it from with one of the exact same color and type, such that the combination of type and color for each gummy bear is independent of the previous gummy bears sold. belinda decides to purchase two gummy bears.

(a) find the probability that both gummy bears purchased by belinda are sugar-free given that the first gummy bear purchased was a sugar-free, orange gummy bear.
(b) find the probability that both gummy bears purchased by belinda are sugar-free given that at least one of them is a sugar-free, orange gummy bear.