- In a school canteen, students can choose from a main course of meat ( \(M\) ), fish ( \(F\) ) or vegetarian ( \(V\) ). They can then choose a drink of either water ( \(W\) ) or juice ( \(J\) ).
The partially completed tree diagram, where \(p\) and \(q\) are probabilities, shows the probabilities of these choices for a randomly selected student.
\section*{Drink}
\begin{figure}[h]
\captionsetup{labelformat=empty}
\caption{Main course}
\includegraphics[alt={},max width=\textwidth]{81d5e460-9559-4d25-aa08-6440559aec83-04_783_1013_593_463}
\end{figure}
- Complete the tree diagram, giving your answers in terms of \(p\) and \(q\) where appropriate.
- Find an expression, in terms of \(p\) and \(q\), for the probability that a randomly selected student chooses water to drink.
The events "choosing a vegetarian main course" and "choosing water to drink" are independent.
- Find a linear equation in terms of \(p\) and \(q\).
A student who has chosen juice to drink is selected at random. The probability that they chose fish for their main course is \(\frac { 7 } { 30 }\)
- Find the value of \(p\) and the value of \(q\).
The canteen manager claims that students who choose water to drink are most likely to choose a fish main course.
- State, showing your working clearly, whether or not the manager's claim is correct.