3. In a company the 200 employees are classified as full-time workers, part-time workers or contractors.\\
The table below shows the number of employees in each category and whether they walk to work or use some form of transport.

\begin{center}
\begin{tabular}{ | c | c | c | }
\cline { 2 - 3 }
\multicolumn{1}{c|}{} & Walk & Transport \\
\hline
Full-time worker & 2 & 8 \\
\hline
Part-time worker & 35 & 75 \\
\hline
Contractor & 30 & 50 \\
\hline
\end{tabular}
\end{center}

The events $F , H$ and $C$ are that an employee is a full-time worker, part-time worker or contractor respectively. Let $W$ be the event that an employee walks to work.

An employee is selected at random.\\
Find
\begin{enumerate}[label=(\alph*)]
\item $\mathrm { P } ( H )$
\item $\mathrm { P } \left( [ F \cap W ] ^ { \prime } \right)$
\item $\mathrm { P } ( W \mid C )$

Let $B$ be the event that an employee uses the bus.\\
Given that $10 \%$ of full-time workers use the bus, $30 \%$ of part-time workers use the bus and $20 \%$ of contractors use the bus,
\item draw a Venn diagram to represent the events $F , H , C$ and $B$,
\item find the probability that a randomly selected employee uses the bus to travel to work.
\end{enumerate}

\hfill \mbox{\textit{Edexcel S1 2013 Q3 [12]}}