Math Count: Kaleb's Legos

Kaleb has a bag containing red, black and white LEGO® bricks. If he has 12 more red bricks than white bricks and 15 fewer white bricks than black bricks, what is the positive difference between the number of red bricks and black bricks in Kaleb’s bag?

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.

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