For all the defective bulbs to be gone, it means that both customers picked a defective bulb. The chance for the first customer to pick a defective bulb is 2/100 = 1/50.
Then if you assume they did pick a defective bulb, there are 99 bulbs of which 1 defective bulb is left. So the chance for the next customer to pick a defective bulb is 1/99.
So the probability of no defective bulbs left is 1/50 * 1/99.
The probability of you picking a defective bulb is trickier - you need to work out 3 different branches of events and add them up.
-no customer picks a defective bulb
-1st customer only picks a defective bulb
-2nd customer only picks a defective bulb