Question 50·Medium·Probability and Conditional Probability

At a school, 240 students are categorized according to whether they have a part-time job. Of the 150 students who have a part-time job, $\frac{2}{5}$ participate in a school sport. Of the remaining students, $\frac{1}{3}$ participate in a school sport.

If one student is selected at random from among the students who participate in a school sport, what is the probability that the selected student has a part-time job?