A forgetful child tries to count the Skittles in a package b

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.

Solution

a)

the number of double counted skittles

if there are 20 skittles in the pack so the number of double counted will be 20

b)

tf there are 20 skittles and he count that plus 20 because he counted double each skilttles and the answer will be 40

20+20 =40