4 In a survey, a large number of young people are asked about their exercise habits. One of these people is selected at random.
- \(G\) is the event that this person goes to the gym.
- \(R\) is the event that this person goes running.
You are given that \(\mathrm { P } ( G ) = 0.24 , \mathrm { P } ( R ) = 0.13\) and \(\mathrm { P } ( G \cap R ) = 0.06\).
- Draw a Venn diagram, showing the events \(G\) and \(R\), and fill in the probability corresponding to each of the four regions of your diagram.
- Determine whether the events \(G\) and \(R\) are independent.
- Find \(\mathrm { P } ( R \mid G )\).