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JEE Main & Advanced Sample Paper JEE Main Sample Paper-9

  • question_answer
    An experiment has 10 equally likely outcomes. Let A and B be two non-empty events of the experiment. If A consists of 4 outcomes, the number of outcomes that B must have so that A and B are independent is

    A)  2, 4 or 8                              

    B)  3, 6 or 9  

    C)  4 or 8                                   

    D)  5 or 10

    Correct Answer: D

    Solution :

    Here, \[n(S)=10,n(A)=4,P(A)=\frac{4}{10}\] Let B have \[m(\ne 0)\] outcomes For A and B to be independent. Now,\[P(A\cap B)=\frac{4}{10}\times \frac{m}{10}\] \[\Rightarrow \]\[P(A\cap B)=\frac{(2m)/5}{10}\] \[\Rightarrow \]\[(A\cap B)\]contains 2 m/5 outcomes. Hence \[\frac{2m}{5}\]must be a natural number  \[\Rightarrow \]m is either 5 or 10       \[[\because \le m\le 10]\]


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