A forgetful child tries to count the Skittles in a package, but he often loses his place and double-counts a Skittle. For each Skittle in the package, the child counts it and then, with probability p, counts it again. The exact number of Skittles in the pack is 20.
a) Find the PMF of R, the number of double-counted Skittles.
(b) Find the PMF of N, the number of Skittles counted by the child.