The inside thread diameter of plastic caps made using an injection molding process is an important quality characteristic. The mold has four cavities. A cap made using cavity i is considered independent from any other cap and can have one of three quality levels: first, second, or third (worst).

The notation P(Fi), P(Si), and P(Ti) represents the probability that a cap made using cavity i has first, second, or third quality, respectively. Given P(F1)  0.4, P(S1)  0.25, P(F2)  0.25, P(S2)  0.30, P(F3)  0.35, P(S3)  0.40, P(F4)  0.5, and P(S4)  0.40,

(a) List the probability of third-level quality for each of the cavities.

(b) What is the probability that one production lot (i.e., a cap from each cavity) has four caps of first quality?

(c) What is the probability that one production lot has four caps with quality at the first or second level?