For independent events ${A_1},\,{A_2},\,..........,{A_n},$ $P({A_i}) = \frac{1}{{i + 1}},$ $i = 1,\,\,2,\,......,\,\,n.$ Then the probability that none of the event will occur, is

  • A

    $\frac{n}{{n + 1}}$

  • B

    $\frac{{n - 1}}{{n + 1}}$

  • C

    $\frac{1}{{n + 1}}$

  • D

    None of these

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  • [IIT 1974]