1. The Venn diagram, where \(w , x , y\) and \(z\) are probabilities, shows the probabilities of a group of students buying each of 3 magazines.

A represents the event that a student buys magazine \(A\) and \(\mathrm { P } ( A ) = 0.60\)
\(B\) represents the event that a student buys magazine \(B\) and \(\mathrm { P } ( B ) = 0.15\)
\(C\) represents the event that a student buys magazine \(C\) and \(\mathrm { P } ( C ) = 0.35\)
\includegraphics[max width=\textwidth, alt={}, center]{77ae01cd-2b58-48ab-889f-272e27ecf99d-06_504_755_641_596}

1. State which two of the three events \(A\), \(B\) and \(C\) are mutually exclusive. The events \(A\) and \(C\) are independent.
2. Show that \(w = 0.21\)
3. Find the value of \(x\), the value of \(y\) and the value of \(z\).
4. Find the probability that a student selected at random buys only one of these magazines.
5. Find the probability that a student selected at random buys magazine \(B\) or magazine \(C\).
6. Find \(\mathrm { P } ( A \mid [ B \cup C ] )\)