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14.Probability
hard
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
Solution
(c) $P$ (non-occurrence of ${A_i}) = 1 – \frac{1}{{i + 1}} = \frac{i}{{i + 1}}$
$\therefore \,\,\,P$ (non-occurrence of any of events)
$ = \left( {\frac{1}{2}} \right)\,.\,\left( {\frac{2}{3}} \right)\,………\left\{ {\frac{n}{{n + 1}}} \right\} = \frac{1}{{n + 1}}.$
Standard 11
Mathematics
