6. Three events \(A , B\) and \(C\) are defined in the sample space \(S\). The events \(A\) and \(B\) are mutually exclusive and \(A\) and \(C\) are independent.
- Draw a Venn diagram to illustrate the relationships between the 3 events and the sample space.
Given that \(\mathrm { P } ( A ) = 0.2 , \mathrm { P } ( B ) = 0.4\) and \(\mathrm { P } ( A \cup C ) = 0.7\), find
- \(\mathrm { P } ( A C )\),
- \(\mathrm { P } ( A \cup B )\),
- \(\mathrm { P } ( C )\).
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