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Question: For independent events A<sub>1</sub>, A<sub>2</sub>... A<sub>n</sub>, P(A<sub>i</sub>) = ![](https:...

For independent events A1, A2... An, P(Ai) =

. Then the probability that none of the event will occur, is

A

nn+1\frac { \mathrm { n } } { \mathrm { n } + 1 }

B

n−1n+1\frac { \mathrm { n } - 1 } { \mathrm { n } + 1 }

C

D

None of these

Answer

Explanation

Solution

P (non-occurrence of Ai) = 1 -

∴ P (non-occurrence of any of events)

= (12)⋅(23)⋯⋅{nn+1}=1n+1\left( \frac { 1 } { 2 } \right) \cdot \left( \frac { 2 } { 3 } \right) \cdots \cdot \left\{ \frac { \mathrm { n } } { \mathrm { n } + 1 } \right\} = \frac { 1 } { \mathrm { n } + 1 }