(i) Probability that the smartphone was defective:

Let D be the event that the smartphone is defective.

P(A) = 0.25, P(B) = 0.35, P(C) = 0.40

P(D|A) = 0.05, P(D|B) = 0.04, P(D|C) = 0.02

Using the law of total probability:

P(D) = P(A) * P(D|A) + P(B) * P(D|B) + P(C) * P(D|C)

P(D) = (0.25 * 0.05) + (0.35 * 0.04) + (0.40 * 0.02)

P(D) = 0.0125 + 0.014 + 0.008

P(D) = 0.0345

(ii) Probability that the defective smartphone was manufactured by company B:

We need to find P(B|D), which is the probability that the smartphone was manufactured by company B given that it is defective.

Using Bayes' theorem:

P(B|D) = [P(D|B) * P(B)] / P(D)

P(B|D) = (0.04 * 0.35) / 0.0345

P(B|D) = 0.014 / 0.0345

P(B|D) = 0.4058 (approximately)