A factory uses three production lines to manufacture cans of a certain type. The accompanying table gives percentages of nonconforming cans, categorized by type of non- conformance, for each of the three lines during a particular lime period.

Line 1 Line 2 Line 3
Blemish 15 12 20
Crack 50 44 40
Pull-Tab problem 21 28 24
Surface Defect 10 8 15
Other 4 8 2

During this period, line 1 produced 500 nonconforming cans, line 2 produced 400 such cans, and line 3 was responsible for 600 nonconforming cans. Suppose that one of these 1500 cans is randomly selected.

(a) What is the probability that the can was produced by line 1? That the reason for non-conformance is a crack?

(b) If the selected can came from line 1, what is the probability that it had a blemish?

(c) Given that the selected can had a surface defect, what is the probability that it came from line 1?