Region counts in a two-set Venn diagram, conditional probabilities and choosing three people without replacement

A racket sports club has \(75\) members. Of these, \(41\) play tennis \((T)\), \(30\) play squash \((Q)\) and \(16\) play neither sport. The Venn diagram shows this information, where \(p\), \(q\) and \(r\) are numbers of members.

1. Find the values of \(p\), \(q\) and \(r\).[4]
2. One member of the club is chosen at random.
   1. Find the probability that this member plays both sports.
   2. Given that this member plays squash, find the probability that this member does not play tennis.[3]
3. Three different members of the club are chosen at random to form a committee.
   1. Find the probability that none of the three members plays tennis.
   2. Hence find the probability that one or more of the three members play tennis.[5]