Doh on the wording.

I suppose "Two bulbs are picked from a randomly selected box." would imply that they were both picked from one box.

That means b) is 50%.

Now, however, the method of solving a chances.

50% chance of box 1 and percentage of 2 defective there is 100/1000 * 99/999 = .990990% (repeating) chance.

50% chance of box 2 and percentage of 2 defective there is 100/2000 * 99/1999 =
.2476238% chance.

Add half the first percent to half the second percent, and there's your answer.

.6193% chance of having 2 defective bulbs. (That is, if you're assuming they're both picked from one box.)

What is it they say about silence being golden?