Instead of sharing with friends, Kaleb decides to share his bag of LEGO bricks with his sister, Kami. Kaleb randomly selects one
brick from the bag and gives it to Kami, then randomly selects another brick from the bag, without replacement, and keeps it for himself. Kaleb continues this random selection and distribution process until he and Kami have the same number of bricks and there is one brick remaining in the bag. If Kaleb started with all 117 LEGO bricks in his bag, what is the probability that the brick left in the bag is black? Express your answer as a common fraction.
