JEE Main & Advanced JEE Main Solved Paper-2014

  • question_answer
    Let A and B be two events such that \[P(\overline{A\cup B})=\frac{1}{16}.P(A\cap B)=\frac{1}{4}\]and\[P(\overline{A})=\frac{1}{4},\]where\[\overline{A}\]stands for the complement of the event A. Then the events A and B are :   JEE Main  Solved  Paper-2014

    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 :

    \[P(\left( \overline{A\cup B} \right)=\frac{1}{6}\]             \[1-P(A\cup B)=\frac{1}{6}\] \[P(A\cup B)=\frac{5}{6}\]                           \[P(A\cap B)=\frac{1}{4}\] \[P(\overline{A})=\frac{1}{4}\]                  \[P(A)=\frac{3}{4}\] \[P(A\cup B)=P(A)+P(B)-P(A\cap B)\] \[\frac{5}{6}=\frac{3}{4}+P(B)-\frac{1}{4}\] \[P(B)=\frac{5}{6}-\frac{1}{2}\]                                  \[P(B)=\frac{1}{3}\] A of B are Independent because \[P(A\cap B)=P(A)P(B).A\]and B has different probability so if is not equally likely.

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