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comment Ranking probability problem
@TMM Imagine we repeat sampling $\langle A, B, C\rangle$ many times, some of them fit the description $P(A>B)=0.7$, $P(B>C)>0.6$ (``pass the observers''). And we want to know in these events, how many of them have $A>C$.
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comment Ranking probability problem
@TMM It means the probability that $A>C>B$ passes the two observers. Since $A>C$, it passes the first observer probability with $70\%$ (she makes a correct observation) probability. Since $C>B$, it passes the second observer with $40\%$ probability (she makes a mistake). And the two events are independent. Hope this solves your problem :)
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revised Ranking probability problem
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revised Ranking probability problem
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answered Ranking probability problem