If A1,A2,....,An are n independent events such that P(Ai)=1i+1,i=1,2,...,n. The probability that none of A1,A2,....An occurs is
A
nn+1
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B
1n+1
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C
less than 1n
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D
noneofthese
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Solution
The correct options are A less than 1n C1n+1 P(A′∩A′2....∩A′n) =P(A′1)P(A′2)...P(A′n) [∵A1,A2,...,An are independent] =(1−12)(1−13)....(1−1n+1) =12×23×34×...×n−1n×nn+1=1n+1<1n.