- A large college produces three magazines.
One magazine is about green issues, one is about equality and one is about sports.
A student at the college is selected at random and the events \(G , E\) and \(S\) are defined as follows
\(G\) is the event that the student reads the magazine about green issues
\(E\) is the event that the student reads the magazine about equality
\(S\) is the event that the student reads the magazine about sports
The Venn diagram, where \(p , q , r\) and \(t\) are probabilities, gives the probability for each subset.
\includegraphics[max width=\textwidth, alt={}, center]{10736735-3050-43eb-9e76-011ca6fa48b8-10_508_862_756_603}
- Find the proportion of students in the college who read exactly one of these magazines.
No students read all three magazines and \(\mathrm { P } ( G ) = 0.25\)
- Find
- the value of \(p\)
- the value of \(q\)
Given that \(\mathrm { P } ( S \mid E ) = \frac { 5 } { 12 }\)
- find
- the value of \(r\)
- the value of \(t\)
- Determine whether or not the events ( \(S \cap E ^ { \prime }\) ) and \(G\) are independent. Show your working clearly.
\section*{Question 4 continued.}
\section*{Question 4 continued.}
\section*{Question 4 continued.}