Probability that neither of two selected members from a group is a lawyer > Of the $700$ members of an organization, $120$ are lawyers. Two members will be selected at random. What is the probability that neither of the members selected will be a lawyer? I know the answer is $(580\cdot 579)/(700\cdot 699)$ My work: Let the event that the first person selected is a lawyer be A. Let the event that the second person selected is a lawyer be B. Assume independence holds. My approach to solving the problem is the probability that neither of the members selected will be a lawyer is 1-P(both members selected will be a lawyer)= $P(\neg A \cap \neg B)=1-P(A \cup B)=1-(P(A)+P(B))$ where $P(A \cap B)=0$. I think the answer is $1-(\frac{120}{700})(\frac{119}{699})$ My solution isn't correct. Why? I assume sampling without replacement.

The probability the first choice is not a lawyer is $580/700$ and the probability that given the first is not a lawyer that the second is also not a lawyer is $579/699$. Multiply these.