2) Here is the 'at least' again. We need to find all the sequences that satisfy.
a)a broken circuit and a good circuit
b) a good circuit and a broken circuit
c) a broken circuit then a broken circuit
a) 5 x 95 or 475
100 99 9900
b) 95 x 5 or 475
100 99 9900
c) 5 x 4 or 20
100 99 9900
Then we add them together and get
970
9900
So the company has a 970 in 9900 chance the inspector will reject the shipment.
You can check your work by coming up with the only possible sequence left.
That sequence is a good circuit then a good circuit:
95 x 94 or 8930
100 99 9900
since these are all the possible 2 choice combinations, they should all add up to 9900.
8930 plus 970 from your answer (2) is 9900.
Always remember to label your answer!!! Writing 970/9900 will not get you all the credit! You have to write out 'there is a 970 in 9900 chance that the inspector will pick out at least 1 defective circuit when 2 are chosen'.