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KVPY Sample Paper KVPY Stream-SX Model Paper-14

  • question_answer
    Let A and B be two events such that \[P\,\overline{(A\cup B)}=\frac{1}{6},\] \[P(A\cap B)=\frac{1}{4}\]and \[P(\overline{A})=\frac{1}{4}\]where \[\overline{A}\] stands for the complement of the event A Then me events A and B are:

    A) mutually exclusive and independent

    B) equally likely but not independent

    C) independent but not equally likely

    D) independent and equally likely

    Correct Answer: C

    Solution :

    \[P(\overline{A\cup B})=\frac{1}{6}\]
    \[P(\overline{A\cup B})=\frac{5}{6},P(A)=\frac{3}{4}\]
    \[P(A\cup B)=P(A)+P(B)-P(A\cup B)=\frac{5}{6}\]
    \[P(B)=\frac{5}{6}-\frac{3}{4}+\frac{1}{4}=\frac{1}{3}\]
    \[P(A\cup B)=P(A).P(B)\]
    \[\frac{1}{4}=\frac{3}{4}\times \frac{1}{3}.\]


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