1. Certain pieces made by an automatic lathe are subject to three kinds of defects X, Y, Z. A sample of 1000 pieces was inspected with the following results: 2.1% had type X defect, 2.4% had type Y defect, and 2.8% had type Z defect. 0.3% had both type X and type Y defects, 0.4% had both type X and type Z defects, and 0.6% had both type Y and type Z defects. 0.1% had type X, type Y , and type Z defects.

Then find:

(a) What percent had none of these defects?

(b) What percent had at least one of these defects?

(c) What percent were free of type X and/or type Y defects?

(d) What percent had not more than one of these defects?