Suppose that a factory has two machines: machine A and machine B. These machines make widgets. Machine A makes 800 per day and 1% of these are defective. Machine B makes 200 per day of which 2% are defective. Then:

(1) The probability that a widget produced by the factory will be defective is

(A) 0.02 (B) 0.012 (C) 0.8 (D)0.03

(2) The probability that the widget is produced by machine A, given that it is defective, is

(A) 0.9 (B) 0.333 (C) 0.03 (D) 0.667