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[Solution Library] 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

Question: 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

\[\begin{aligned} & A=\text{ Voter is Republican} \\ & B=\text{ Voted for Candidate X} \\ \end{aligned}\]
  1. Write values for \(\Pr \left( A \right),\Pr \left( {{A}^{C}} \right),\Pr \left( B|A \right)\) and \(\Pr \left( B|{{A}^{C}} \right)\).
  2. Find \(\Pr \left( A\cap B \right)\) and write in word what outcome it represents.
  3. Find \(\Pr \left( {{A}^{C}}\cap B \right)\) and write in word what outcome it represents.
  4. Find \(\Pr \left( B \right)\)
  5. What percentage of the vote did the Candidate X receive?

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