Three assembly lines for the same product have different nonconformance rates: p = .1 for Line A, p = .15 for Line B, and p = .2 for Line C. One of the three lines will be selected at random (but you don’t know which). Let X = the number of items inspected from the selected line until a nonconforming one is found.
a. What is the distribution of X, as a function of the unknown p?
b. Express the given information as a prior distribution for the parameter p.

c. It is determined that the 8th item coming off the randomly selected line is the first nonconforming one. Use this information to determine the posterior distribution of p.