A seam weld is inspected using a nondestructive evaluation method and was determined to have defects following a Poisson process with a rate λ = 0.05 per ft. A pressure vessel contains 20 ft of this seam weld.

(a) What is probability that the pressure vessel will be free of defects in this seam weld?

(b) Five pressure vessels were delivered to an industrial plant, what is the probability that three out of the five pressure vessels will not have weld defects in the seams?

(c) What is the probability of not having defects in the seam welds of the five pressure vessels if treated as one 100-ft seam weld? Compare the two answers from

(b) and (c), and discuss.