Homework 2: Definition of Probability

1. Section 1.5, #3, 4, 7.
2. Assume that \(P(A\cap B) = 0.3\), \(P(A\cap C) = 0.4\), \(P(B\cap C) = 0.3\), \(P(A^c\cap B^c\cap C) = 0\), \(P(C)= 0.6\), \(P(A\cup C) = 0.8\), and \(P(B^c\cup C) = 0.7\).
   1. Fill in all of the probabilities in the Venn diagram for \(A\), \(B\), and \(C\).
   2. Find \(P(B^c)\), \(P(A\cap B\cap C)\), and \(P(A)\).