Q.Suppose that five good fuses and two defective ones have been mixed up. To find the defective fuses, we test them one-by-one, at random and without replacement. What is the probability that we are lucky and find both of the defective fuses in the first two tests?

7 fuses total (5 good, 2 defective). $P(\text{1st defective})=2/7$. After removing one defective fuse, 6 remain with 1 defective: $P(\text{2nd defective}/\text{1st defective})=1/6$. $P(\text{both defective found …

Multiplication theorem for sequential draws without replacement, since finding both defectives in the first two tests requ …

Using $2/7\times2/7$ (as if with replacement or as if 2 defectives could be drawn independently at the same rate), …