- Isobel plays football for a local team. Sometimes her parents attend matches to watch her play.
- \(A\) is the event that Isobel's parents watch a match.
- \(B\) is the event that Isobel scores in a match.
You are given that \(\mathrm { P } ( B \mid A ) = \frac { 3 } { 7 }\) and \(\mathrm { P } ( A ) = \frac { 7 } { 10 }\).
- Calculate \(\mathrm { P } ( A \cap B )\).
The probability that Isobel does not score and her parents do not attend is 0.1 .
- Draw a Venn diagram showing the events \(A\) and \(B\), and mark in the probability corresponding to each of the regions of your diagram.
- Are events \(A\) and \(B\) independent? Give a reason for your answer.
- By comparing \(\mathrm { P } ( B \backslash A )\) with \(\mathrm { P } ( B )\), explain why Isobel should ask her parents not to attend.
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