(Solved): Suppose that we have a sample space with five equally likely experimental outcomes: \( E_{1}, E_{2 ...

Suppose that we have a sample space with five equally likely experimental outcomes: \( E_{1}, E_{2}, E_{3}, E_{4}, E_{5} \). Let \[ \begin{array}{l} A=\left\{E_{2}, E_{3}\right\} \\ B=\left\{E_{1}, E_{4}\right\} \\ C=\left\{E_{1}, E_{3}, E_{5}\right\} . \end{array} \] (a) Find \( P(A), P(B) \), and \( P(C) \). \[ \begin{array}{l} P(A)= \\ P(B)= \\ P(C)= \end{array} \] (b) Find \( P(A \cup B) \). \[ P(A \cup B)= \] Are \( A \) and \( B \) mutually exclusive? They mutually exclusive. (c) Find \( A^{C} \). (Enter your answer in set notation.) \[ A^{C}= \] Find \( C^{C} \). (Enter your answer in set notation.) \[ C^{C}= \] Find \( P\left(A^{C}\right) \) and \( P\left(C^{C}\right) \) \[ P\left(A^{C}\right)= \]