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JEE Main & Advanced Mathematics Probability Question Bank Definition of various terms

  • question_answer
    Let A, B, C be three mutually independent events. Consider the two statements \[{{S}_{1}}\]and \[{{S}_{2}}\]                 \[{{S}_{1}}\,\,:\,\,A\] and \[B\cup C\] are independent                 \[{{S}_{2}}\,\,:\,\,A\] and \[B\cap C\] are independent                 Then [IIT 1994]

    A)                 Both \[{{S}_{1}}\] and \[{{S}_{2}}\] are true

    B)                 Only \[{{S}_{1}}\] is true

    C)                 Only \[{{S}_{2}}\] is true

    D)                 Neither \[{{S}_{1}}\] nor \[{{S}_{2}}\] is true

    Correct Answer: A

    Solution :

                       \[B\cup C\] is independent to \[A,\] so \[{{S}_{1}}\] is true                 \[B\cap C\] is also independent to \[A,\] so \[{{S}_{2}}\] is true.


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