How to calculate this question.

#1
I was unable to figure out which method should I use to calculate the question. I tried to make it into Venn diagram and into table still unable to sort it out :(

A producer of a certain type of medical instruments ships to suppliers in lots of twenty. Suppose that 60% of all such lots contain no defective instruments, 30% contain one defective instrument, and 10% contain two defective instruments. A lot is picked, two instruments from the lot are randomly selected and tested, and neither is defective.
Find the probability that zero defective instruments exists in the lot.
 
#2
Try drawing a tree, or listing the possibilities for neither sample defective.
Find the probability of -
0 defective lot picked and neither sample is defective = p0
1 defective lot picked and neither sample is defective = p1
2 defective lot picked and neither sample is defective = p2
Then the probability that you have a 0 defective lot is p0/(p0+p1+p2)
kat