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

\[\begin{aligned} & A=\text{ Voter is Republican} \\ & B=\text{ Voted for Candidate X} \\ \end{aligned}\]

(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?