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JEE Main & Advanced Sample Paper JEE Main Sample Paper-25

  • question_answer
    Let \[{{A}_{i}}\], where \[i=\] 1, 2, 3,......n, be n independent event such that \[P(A)=\frac{1}{i+1}\], then probability that none of the event \[{{A}_{1}},{{A}_{2}},......,{{A}_{n}}\], occur is

    A)  \[\frac{n}{n+1}\]                                 

    B)  \[\frac{n-1}{n+1}\]

    C)  \[\frac{1}{n+1}\]                                 

    D)  \[\frac{1}{n-1}\]

    Correct Answer: C

    Solution :

    \[P({{\overline{A}}_{i}})=1-\frac{1}{i+1}=\frac{i}{i+1}\]P (none of event occur) \[P({{\overline{A}}_{i}})\,P({{\overline{A}}_{2}}).....P({{\overline{A}}_{n}})\,=\frac{1}{2}\,\times \frac{2}{3}.........\frac{n}{n+1}\,=\frac{1}{n+1}\]


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