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JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1
The probability of the choosing an integer λ\lambda, randomly from the integers 1,2,3,…2n1,2,3, \ldots 2{n} is proportional to log⁡λ\log \lambda. The conditional probability of choosing integer 2, given that an even integer is choosen is
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Correct option: B
log⁡2nlog⁡2+log⁡(n!)\frac{\log 2}{n \log 2+\log (n !)}
Option B (log⁡2nlog⁡2+log⁡(n!)\frac{\log 2}{n \log 2+\log (n !)}) is correct because it is the conditional probability calculated using the given proportionality.

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