The manufacturer rejects the lot if 10% or more of the units are defective.
In the lot being considered 11% of units are defective and it should be rejected.
Using the quality control inspector's criterion, 10 units are chosen from the lot and if 2 or more are defective the lot is rejected. When 10 units are chosen from the lot under consideration there 10*0.11 = 1.1 defective units; as the number of defective units has to be a whole number there are 2 defective units. When 2 units are chosen from this lot, the probability that both the units chosen are defective is (2/10)*(1/9) = 1/45
The probability that the correct decision is taken in this case using the quality control inspector's method is 1/45 = 0.022.