Define the events A; FEE; FCS;MEE, and MCS as in Section 16.

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Define the events A; FEE; FCS;MEE, and MCS as in Section 16.5.8. In these terms, the plaintiff in a discrimination suit against a university makes the argument that in both departments, the probability that a woman is granted tenure is less than the probability for a man. That is,

The university’s defense attorneys retort that overall, a woman applicant is more likely to be granted tenure than a man, namely, that 

The judge then interrupts the trial and calls the plaintiff and defense attorneys to a conference in his office to resolve what he thinks are contradictory statements of facts about the tenure data. The judge points out that:

which directly contradicts the university’s position (16.21)! But the judge is mistaken; an example where the plaintiff and defense assertions are all true appears in Section 16.5.8. What is the mistake in the judge’s proof?