If the Coast Guard randomly inspects 2 of the 10 ships, what is the probability that it inspects both of the drug-carrying ships?

Question

Suppose 10 cargo ships arrive at Port of Miami, and 2 of them are carrying drugs. If the Coast Guard randomly inspects 2 of the 10 ships, what is the probability that it inspects both of the drug-carrying ships? Give a convincing argument to support your answer.

Answer 1

2 out of 10 chance of getting 1 drug cargo ship

then 1 out 9 of getting the 2nd

2/10 x 1/9 - 2/90 = 1/45 chance of getting both

= 2 2/9 % probability