1. (a) State one disadvantage of using quota sampling compared with simple random sampling.

In a university 8\% of students are members of the university dance club.
A random sample of 36 students is taken from the university.
The random variable \(X\) represents the number of these students who are members of the dance club.
(b) Using a suitable model for \(X\), find

1. \(\mathrm { P } ( X = 4 )\)
2. \(\mathrm { P } ( X \geqslant 7 )\) Only 40\% of the university dance club members can dance the tango.
   (c) Find the probability that a student is a member of the university dance club and can dance the tango. A random sample of 50 students is taken from the university.
   (d) Find the probability that fewer than 3 of these students are members of the university dance club and can dance the tango. \section*{Question 1 continued.}