Question: Problem 7.36: In a recent election, 55% of the voters were republican, and 45% were not. Of the republicans, 80% voted for candidate X, and of the non-republican, 10% voted for candidate X. Consider a randomly selected voter. Define
\[\begin{align}
& A=\text{ Voter is Republican} \\
& B=\text{ Voted for Candidate X} \\
\end{align}\]
(a) Write values for \(\Pr \left( A \right),\Pr \left( {{A}^{C}} \right),\Pr \left( B|A \right)\) and \(\Pr \left( B|{{A}^{C}} \right)\).
(b) Find \(\Pr \left( A\cap B \right)\) and write in word what outcome it represents.
(c) Find \(\Pr \left( {{A}^{C}}\cap B \right)\) and write in word what outcome it represents.
(d) Find \(\Pr \left( B \right)\)
(e) What percentage of the vote did the Candidate X receive?
Deliverables: Word Document
