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JCECE Engineering JCECE Engineering Solved Paper-2004

  • question_answer
    If \[P(A)=P(B)=x\] and\[P(A\cap B)=P(A'\cap B')=\frac{1}{3}\], then \[x\] is equal to:

    A) \[1/2\]                                 

    B) \[1/4\]

    C) \[1/3\]                                 

    D) \[1/6\]

    Correct Answer: A

    Solution :

    We know,                 \[P(A'\cap B')=1-P(A\cup B)\] \[\Rightarrow \]               \[P(A\cup B)=1-\frac{1}{3}=\frac{2}{3}\] \[\therefore \]  \[P(A\cup B)=P(A)+P(B)-P(A\cap B)\] \[\Rightarrow \]               \[\frac{2}{3}=x+x-\frac{1}{3}\] \[\Rightarrow \]               \[x=\frac{1}{2}\]


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