Question: Check whether for 3 arbitrary random events (A, B), and (C) the following constellations of probabilities can be true: (1) (P(A)=0.6, P(A cap B)=0.2), and
Check whether for 3 arbitrary random events \(A, B\), and \(C\) the following constellations of probabilities can be true:
(1) \(P(A)=0.6, P(A \cap B)=0.2\), and \(P(A \cap \bar{B})=0.5\),
(2) \(P(A)=0.6, P(B)=0.4, P(A \cap B)=0\), and \(P(A \cap B \cap C)=0.1\),
(3) \(P(A \cup B \cup C)=0.68\) and \(P(A \cap B)=P(A \cap C)=1\).
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