A quality control department of a tire manufacturing company regularly conducts quality control checks at specified periods on the products it manufactures. Historically, the failure rate for tires that the company manufactures is 5%. Suppose a random sample of 3 tires is selected. Let X be the random variable that denote a defective tire. Answer the following questions.

(a) Construct the probability distribution table associated with X

(b) From the table in part (a) Find the probability that

(i) none of the tires are defective?

(ii) exactly 2 of the tires are defective?

(iii) at most two of the tires are defective?

(iv) two or more of the tires are defective?