5 Each day Anna drives to work.
- \(R\) is the event that it is raining.
- \(L\) is the event that Anna arrives at work late.
You are given that \(\mathrm { P } ( R ) = 0.36 , \mathrm { P } ( L ) = 0.25\) and \(\mathrm { P } ( R \cap L ) = 0.2\).
- Determine whether the events \(R\) and \(L\) are independent.
- Draw a Venn diagram showing the events \(R\) and \(L\). Fill in the probability corresponding to each of the four regions of your diagram.
- Find \(\mathrm { P } ( L \mid R )\). State what this probability represents.