There are 180 students at a college following a general course in computing - Edexcel - A-Level Maths Statistics - Question 4 - 2010 - Paper 1

To find the probability that a student takes none of the three extra options, we use the formula:

$P(None) = \frac{Number\ of\ students\ with\ no\ options}{Total\ number\ of\ students}$

Thus,

$P(None) = \frac{16}{180} = \frac{4}{45}$

To find the probability that a student takes only networking, we can represent this as:

$P(Networking\ Only) = \frac{Number\ of\ students\ in\ only\ networking}{Total\ number\ of\ students}$

There are 9 students that take networking only:

$P(Networking\ Only) = \frac{9}{180} = \frac{1}{20}$

Given that a student wants to become a technician, we focus on those who take Systems Support and Networking which totals:

$Total\ (Technicians) = (40 + 4) = 44$

To find the probability that this student takes all three options:

$P(All\ Three) = \frac{Number\ of\ students\ taking\ all\ three\ options}{Total\ Technicians} = \frac{4}{44} = \frac{1}{11}$