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Question

Assertion: Given Ei(i=1,2,.......n) are n independent events such that P(¯Ei)=ii+1,1in, then the probability that none of the n events occur is nn+1

Reason: Probability of occurence of all independent events is equal to the product of the probabilities of individual events.

A
Both Assertion & Reason are individually true & Reason is correct explanation of Assertion
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B
Both Assertion & Reason are individually true but Reason is not correct (proper) explanation of Assertion
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C
Assertion is true but Reason is false
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D
Assertion is false but Reason is true
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Solution

The correct option is D Assertion is false but Reason is true
P(¯Ei)=i1+i(i=1,2,3....,n)
P(¯E1)=12,P(¯E2)=23,P(¯E3)=34,....P(¯En)=nn+1
P(¯E1¯E2¯E3.....¯En)=12.23.34....n1n.nn+1=1n+1
Assertion (A) is false but Reason (R) is true.

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