4. Events \(A\) and \(B\) are shown in the Venn diagram below
where \(x , y , 0.10\) and 0.32 are probabilities.
\includegraphics[max width=\textwidth, alt={}, center]{c58f3e88-2dbc-40d6-a966-a5765a7c67ba-08_467_798_408_575}
- Find an expression in terms of \(x\) for
- \(\mathrm { P } ( A )\)
- \(\mathrm { P } ( B \mid A )\)
- Find an expression in terms of \(x\) and \(y\) for \(\mathrm { P } ( A \cup B )\)
Given that \(\mathrm { P } ( A ) = 2 \mathrm { P } ( B )\)
- find the value of \(x\) and the value of \(y\)