(CONDITIONAL PROBABILITY) Which probability would you expect to be greater?

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SUMMARY

The discussion centers on comparing two conditional probabilities: (a) the probability that a person is smart given that they have a university degree, and (b) the probability that a person has a university degree given that they are smart. Participants agree that (a) is likely greater than (b), attributing this to the relatively low global proportion of individuals with university degrees. The conversation emphasizes the importance of data in making definitive conclusions about these probabilities.

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Which probability would you expect to be greater?

(a) The probability that a person is smart given that he has a university degree,

OR,

(b) the probability that a person has a university degree given that he is smart? I would say (a)>(b), but, what would you say?
 
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With no data, we're just guessing aren't we. I would guess in agreement with you because I would guess that the proportion of people with university degrees worldwide isn't that large, smart or not.
 

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