3 Each weekday, Marta travels to school by bus. Sometimes she arrives late.

• \(L\) is the event that Marta arrives late.
• \(R\) is the event that it is raining.

You are given that \(\mathrm { P } ( L ) = 0.15 , \mathrm { P } ( R ) = 0.22\) and \(\mathrm { P } ( L \mid R ) = 0.45\).

1. Use this information to show that the events \(L\) and \(R\) are not independent.
2. Find \(\mathrm { P } ( L \cap R )\).
3. Draw a Venn diagram showing the events \(L\) and \(R\), and fill in the probability corresponding to each of the four regions of your diagram.