Is this the right use of Bayes Law and approach for solving this problem? Problem: There are $25$ skateboarders, $15$ basketball players, and $10$ volleyball players in training camp. They have to meet the requirements of qualification. The probability that they will qualify is: $0.9$ for skateboarder, $0.8$ for basketball player, $0.7$ for volleyball player. Find the probability, that chosen athlete will qualify and that it will be done by volleyball player. Solution: It seems to me that the fact that I am asked for probability, that the athlete will qualify, knowing that it will be volleyball player, indicates that I have to use Bayes Law. So, Q-athlete will qualify V-athlete chosen will be volleyball player $$P(Q|V)=\frac{P(V|Q)\cdot P(Q)}{P(V)}$$ $$P(Q)=0.7$$ $$P(V)=\frac{10}{50}=0.2$$ So what would be $P(V|Q)$? Is this the right approach?

Hint: $P(A \text{ and } B) = P(A \cap B)=P(A \mid B)P(B)=P(B \mid A)P(A)$