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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class12  >>  Probability
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If A,B,C are three events with $P(C)=0$ then $ P(A \cup B \cup C )=$

$\begin {array} {1 1} (1)\;P(A)+P(B) & \quad (2)\;P(A)+P(C) \\ (3)\;P(A)+P(B)-P(A \cap B) & \quad (4)\;None\: of \: these \end {array}$

 

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1 Answer

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Since $ A \cap C \underline{c} C$
$ P(A \cap C ) \leq P(C)=0$
Also $ P(A \cap C ) \geq 0$
$ \therefore P(A \cap C)=0=P(A)\: P(C)$
Similarly $ P(B \cap C ) = 0$
$ P ( A \cap B \cap C ) = 0$
$ \therefore P ( A \cup B \cup C ) = P(A)+P(B)+P(C)-P(B \cap C )$
$-P(C \cap A)-P( A \cap B )+P(A \cap B \cap C )$
$ = P(A)+P(B)-P(A \cap B)$
Ans : (3)

 

answered Jan 2, 2014 by thanvigandhi_1
 

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