Complete a Venn diagram, calculate conditional probability, test independence and sample without replacement.

In a group of \(16\) students, \(12\) take art and \(8\) take music. One student takes neither art nor music. The Venn diagram below shows the events art and music. The values \(p, q, r\) and \(s\) represent numbers of students.

1. [5]

   1. Write down the value of \(s\).

   2. Find the value of \(q\).

   3. Write down the value of \(p\) and of \(r\).

2. [4]
   1. A student is selected at random. Given that the student takes music, write down the probability the student takes art.
   2. Hence, show that taking music and taking art are not independent events.
3. Two students are selected at random, one after the other. Find the probability that the first student takes only music and the second student takes only art.[4]