Question 9·Hard·Probability and Conditional Probability

At a learning center, 240 students may enroll in the Design workshop, the Robotics workshop, both workshops, or neither workshop.

If a student is selected at random from the students enrolled in exactly one of the two workshops, the probability that the student is enrolled in Design is $\frac{4}{7}$. What is the probability that a student selected at random from the students not enrolled in Robotics is enrolled in Design?