Moderate -0.8 This is a straightforward probability and combinatorics question requiring only standard techniques: Venn diagrams for conditional probability and basic combination calculations. All parts are routine textbook exercises with no novel problem-solving required, making it easier than average A-level standard.
A music club has 200 members. 75 members play the piano, 130 members like Elgar, and 30 members do not play the piano, nor do they like Elgar.
Calculate the probability that a member chosen at random plays the piano but does not like Elgar. [3]
Calculate the probability that a member chosen at random plays the piano given that this member likes Elgar. [2]
The music club is organising a concert. The programme is to consist of 7 pieces of music which are to be selected from 9 classical pieces and 6 modern pieces. Find the number of different concert programmes that can be produced if
there are no restrictions, [2]
the programme must consist of 5 classical pieces and 2 modern pieces, [2]
there are to be more modern pieces than classical pieces. [3]
\begin{enumerate}[label=(\alph*)]
\item A music club has 200 members. 75 members play the piano, 130 members like Elgar, and 30 members do not play the piano, nor do they like Elgar.
\begin{enumerate}[label=(\roman*)]
\item Calculate the probability that a member chosen at random plays the piano but does not like Elgar. [3]
\item Calculate the probability that a member chosen at random plays the piano given that this member likes Elgar. [2]
\end{enumerate}
\item The music club is organising a concert. The programme is to consist of 7 pieces of music which are to be selected from 9 classical pieces and 6 modern pieces. Find the number of different concert programmes that can be produced if
\begin{enumerate}[label=(\roman*)]
\item there are no restrictions, [2]
\item the programme must consist of 5 classical pieces and 2 modern pieces, [2]
\item there are to be more modern pieces than classical pieces. [3]
\end{enumerate}
\end{enumerate}
\hfill \mbox{\textit{Pre-U Pre-U 9794/3 2020 Q2 [12]}}