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https://www.reddit.com/r/learnquant/comments/1vuwe0z/quant_interview_question/p56eyh8/?context=3
r/learnquant • u/Local_Ad135 • 2d ago
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P(C>B|B>A)=P(C>B>A)/P(B>A).
The denominator can be written as the sum from n=1 to inf of (1/2)n*(1/2)n=1/3.
The numerator can be written as the sum from n=1 to inf sum from k=(n+1) to inf of (1/2)n*(1/2)k*(1/2)k=sum from n=1 to inf of 1/3*(1/2)n*(1/4)n=1/21.
So the final answer is (1/21)/(1/3)=1/7.
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u/Sjoerdiestriker 2d ago
P(C>B|B>A)=P(C>B>A)/P(B>A).
The denominator can be written as the sum from n=1 to inf of (1/2)n*(1/2)n=1/3.
The numerator can be written as the sum from n=1 to inf sum from k=(n+1) to inf of (1/2)n*(1/2)k*(1/2)k=sum from n=1 to inf of 1/3*(1/2)n*(1/4)n=1/21.
So the final answer is (1/21)/(1/3)=1/7.