If A1, A2, A3−−−−An are independent events such that PAk=1K+1 ; K= 1, 2, 3--- n then the probability that none of the A1, A2, A3−−−−An occur, is

PA1¯∩A2¯∩A3¯∩−−−−−An¯=PA¯1PA¯2PA¯3−−−−PA¯n=122334−−−−−nn+1=1n+1

If A1, A2, A3−−−−An are independent events such that PAk=1K+1 ; K= 1, 2, 3--- n then the probability that none of the A1, A2, A3−−−−An occur, is

PA1¯∩A2¯∩A3¯∩−−−−−An¯=PA¯1PA¯2PA¯3−−−−PA¯n=122334−−−−−nn+1=1n+1

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If $A_{1}, A_{2}, A_{3} - - - - A_{n}$ are independent events such that $P (A_{k}) = \frac{1}{K + 1}$ ; K= 1, 2, 3--- n then the probability that none of the $A_{1}, A_{2}, A_{3} - - - - A_{n}$ occur, is

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

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

$\frac{1}{n!}$

$\frac{1}{{(n + 1)}^{2}}$

answer is A.

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$\begin{array}{l} P (\bar{A_{1}} \cap \bar{A_{2}} \cap \bar{A_{3}} \cap - - - - - \bar{A_{n}}) \\ = P ({\bar{A}}_{1}) P ({\bar{A}}_{2}) P ({\bar{A}}_{3}) - - - - P ({\bar{A}}_{n}) \end{array}$

$= \frac{1}{2} (\frac{2}{3}) (\frac{3}{4}) - - - - - \frac{n}{n + 1} = \frac{1}{n + 1}$

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If A1, A2, A3−−−−An are independent events such that PAk=1K+1 ; K= 1, 2, 3--- n then the probability that none of the A1, A2, A3−−−−An occur, is

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If $A_{1}, A_{2}, A_{3} - - - - A_{n}$ are independent events such that $P (A_{k}) = \frac{1}{K + 1}$ ; K= 1, 2, 3--- n then the probability that none of the $A_{1}, A_{2}, A_{3} - - - - A_{n}$ occur, is