3 Each weekday Alan drives to work. On his journey, he goes over a level crossing. Sometimes he has to wait at the level crossing for a train to pass.

• \(W\) is the event that Alan has to wait at the level crossing.
• \(L\) is the event that Alan is late for work.

You are given that \(\mathrm { P } ( L \mid W ) = 0.4 , \mathrm { P } ( W ) = 0.07\) and \(\mathrm { P } ( L \cup W ) = 0.08\).

1. Calculate \(\mathrm { P } ( L \cap W )\).
2. Draw a Venn diagram, showing the events \(L\) and \(W\). Fill in the probability corresponding to each of the four regions of your diagram.
3. Determine whether the events \(L\) and \(W\) are independent, explaining your method clearly.