Concept
How does learning that the winner was a UMW student change the probability of a junior winner?
Stephen Davies, Ph.D. Version 2.2.2 Through Discrete Mathematics A Cool Brisk Walk / Chapter 1
"By the definition of conditional probability, Pr(J | U) = Pr(J ∩ U) / Pr(U) = .1 / .7 = 1/7 ≈ .143. This is quite a bit lower than the .4 we computed for Pr(J) in item 10. So if you knew nothing about the winner other than the swimmers’ baseline probabilities, you’d estimate a 40% chance of a junior winning—but if you learned the winner was a UMW student, your estimate of a junior winner would drop down to nearly 14%."
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