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December 24th, 2017, 11:09 AM  #1 
Newbie Joined: Dec 2017 From: US Posts: 1 Thanks: 0  Which is true?
Assume there are three events, A, B, and C. Also, assume that P(A∨B)=0.5, and P(C)=0.5. Which of the following is true? 1. A and B are disjoint 2. A, B, and C are disjoint 3. P(C)>P(A∧B) 4. P(A∧B∧C)<0.5 5. None of these I'm trying to understand and think of all possible probabilities to either prove or refute the options as correct or wrong. Help? 
December 24th, 2017, 12:35 PM  #2  
Senior Member Joined: Sep 2015 From: USA Posts: 1,781 Thanks: 919  Quote:
1) not enough information 2) not enough information, $A \cup B$ and $C$ are disjoint 3) no, if $A=B$ then $P[A \cap B] = 0.5 = P[C]$ 4) Yes, $(A \cap B) \subseteq (A \cup B),~(A \cup B) \cap C = \emptyset$ so $(A \cap B \cap C = \emptyset) \Rightarrow P[A \cap B \cap C] = 0$  

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