Sandro has four possible ways home from school.

From school he takes either a bus or a train.
The probability that he will go by train is $\dfrac{3}{5}$.

If he goes by train, he completes the second part of the journey by walking or by
getting a lift. The probability that he gets a lift is $\dfrac{1}{4}$.

If he catches a bus, the second part of his journey can be complete by catching
another bus or he can walk.
The probability that he will walk is $\dfrac{7}{8}$.

\begin{enumerate}
    \item \nbPointsEnumi{3}Draw a tree diagram showing all of the possible outcomes of Sandro's journey
from school
\end{enumerate}

Using the tree diagram calculate the probability that Sandro:

\begin{enumerate}[resume]
    \item \nbPointsEnumi{3}Catches a bus from school and then walks
    
    \item \nbPointsEnumi{3}Walks for part of his journey home
    
    \item \nbPointsEnumi{3}Given that he walks the second part of the journey, what is the probability
that he caught the bus?
\end{enumerate}
