4. There are 180 students at a college following a general course in computing. Students on this course can choose to take up to three extra options.
\begin{displayquote}
112 take systems support,
70 take developing software,
81 take networking,
35 take developing software and systems support,
28 take networking and developing software,
40 take systems support and networking,
4 take all three extra options.
- In the space below, draw a Venn diagram to represent this information.
\end{displayquote}
A student from the course is chosen at random.
Find the probability that this student takes
- none of the three extra options,
- networking only.
Students who want to become technicians take systems support and networking. Given that a randomly chosen student wants to become a technician,
- find the probability that this student takes all three extra options.