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JEE Main & Advanced JEE Main Paper (Held On 11 April 2014)

  • question_answer
    A set S contains 7 elements. A non-empty subset A of S and an element x of S are chosen at random. Then the probability that \[x\in A\]is:   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

    A) \[\frac{1}{2}\]                                   

    B) \[\frac{64}{127}\]

    C) \[\frac{63}{128}\]                                            

    D) \[\frac{31}{128}\]

    Correct Answer: B

    Solution :

    Let\[S=\{{{x}_{1}},{{x}_{2}},{{x}_{3}},{{x}_{4}},{{x}_{5}},{{x}_{6}},{{x}_{7}}\}\] Let the chosen element be \[{{x}_{i}}.\] Total number of subsets of \[S={{2}^{7}}=128\] No. of non-empty subsets of \[S=128-1=127\] We need to find number of those subsets that contains \[{{x}_{i}}\].
    2 2 2 2 1 2 2
     \[{{x}_{1}}{{x}_{2}}\]-------\[{{x}_{i}}\] ----\[{{x}_{7}}\] For those subsets containing xi, each element has 2 choices. i.e., (included or not included) in subset, However as the subset must contain \[{{x}_{i}},{{x}_{i}}\]has only one choice. (included one) So, total no. of subsets containing \[{{x}_{i}}=2\times 2\times 2\times 1\times 2\times 2=64\] Required prob \[=\frac{\text{No}\text{.}\,\text{of}\,\text{subsets}\,\text{containing}\,{{\text{x}}_{\text{i}}}}{\,\text{Total}\,\text{no}\text{.}\,\text{of}\,\text{non-empty}\,\text{subsets}}\]\[=\frac{64}{127}\]


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