A quality-control engineer wants to check whether (in accordance with specifications) \(95 \%\) of the electronic components shipped by his company are in good working condition. To this end, he randomly selects 15 from each large lot ready to be shipped and passes the lot if the selected components are all in good working condition; otherwise, each of the components in the lot is checked. Find the probabilities that the quality-control engineer will commit the error of

(a) holding a lot for further inspection even though \(95 \%\) of the components are in good working condition;

(b) letting a lot pass through without further inspection even though only \(90 \%\) of the components are in good working condition;

(c) letting a lot pass through without further inspection even though only \(80 \%\) of the components are in good condition.