JEE Main & Advanced Sample Paper JEE Main Sample Paper-35

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

    A)  mutually exclusive and independent.

    B)  independent but not equally likely.

    C)  equally likely but not independent.

    D)  equally likely and mutually exclusive.

    Correct Answer: B

    Solution :

    \[P(\overline{A\cup B})\,=\frac{1}{6}\Rightarrow \,1-6(P\cup B)\,=\frac{1}{6}\] \[\Rightarrow \,\,(1-P(A))\,-P(B)\,+P(A\cap B)\,=\frac{1}{6}\] \[\Rightarrow \,P(\overline{A})\,-P(B)\,+P(A\cap B)\,=\frac{1}{6}\] \[\Rightarrow \,\frac{1}{4}\,-P(B)\,+\frac{1}{4}\,=\frac{1}{6}\] \[\Rightarrow P(B)=\frac{1}{3}\,and\,P(A)=1-\frac{1}{4}=\frac{3}{4}\]             As \[P(A\cap B)\,=P(A)\,P(B)\] So, events A and B are independent events but they are not equally likely.

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