Moderate -0.8 This is a straightforward application of the inclusion-exclusion principle with all values provided directly. Students simply need to fill in a three-set Venn diagram by working from the center outward, then perform basic probability calculations. The conditional probability in part (c) is also routine. This requires less problem-solving than a typical A-level question.
3. 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.
\end{displayquote}
a Draw a Venn diagram to represent this information.
A student from the course is chosen at random.
b Find the probability that this student takes
i none of the three extra options
ii networking only.
Students who take systems support and networking are eligible to become technicians.
c Given that the randomly chosen student is eligible to become a technician, find the probability that this student takes all three extra options. [0pt]
3. 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.
\end{displayquote}
a Draw a Venn diagram to represent this information.
A student from the course is chosen at random.\\
b Find the probability that this student takes\\
i none of the three extra options\\
ii networking only.
Students who take systems support and networking are eligible to become technicians.\\
c Given that the randomly chosen student is eligible to become a technician, find the probability that this student takes all three extra options.\\[0pt]
\\
\hfill \mbox{\textit{SPS SPS SM Statistics 2021 Q3 [7]}}