3. For the events $A$ and $B$,
\begin{enumerate}[label=(\alph*)]
\item explain in words the meaning of the term $\mathrm { P } \left( \begin{array} { l l } B & A \end{array} \right)$,
\item sketch a Venn diagram to illustrate the relationship $\mathrm { P } \left( \begin{array} { l l } B & A \end{array} \right) = 0$.

Three companies operate a bus service along a busy main road. Amber buses run $50 \%$ of the service and $2 \%$ of their buses are more than 5 minutes late. Blunder buses run $30 \%$ of the service and $10 \%$ of their buses are more than 5 minutes late. Clipper buses run the remainder of the service and only $1 \%$ of their buses run more than 5 minutes late.

Jean is waiting for a bus on the main road.
\item Find the probability that the first bus to arrive is an Amber bus that is more than 5 minutes late.

Let $A , B$ and $C$ denote the events that Jean catches an Amber bus, a Blunder bus and a Clipper bus respectively. Let $L$ denote the event that Jean catches a bus that is more than 5 minutes late.
\item Draw a Venn diagram to represent the events $A , B , \mathrm { C }$ and $L$. Calculate the probabilities associated with each region and write them in the appropriate places on the Venn diagram.
\item Find the probability that Jean catches a bus that is more than 5 minutes late.
\end{enumerate}

\hfill \mbox{\textit{Edexcel S1 2002 Q3 [12]}}