Chapter 16 Events and Probability Spaces572
is less than the probability for a man. That is,
PrAjFEE<PrAjMEEand (16.18)
PrAjFCS<PrAjMCS: (16.19)
The university’s defence attornies retort thatoverall, a woman applicant ismore
likely to be granted tenure than a man, namely, that
PrAjFEE[FCS>PrAjMEE[MCS: (16.20)
The judge then interrupts the trial and calls the plaintiff and defence attornies 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:
PrAjFEE[FCSDPrAjFEECPrAjFCS(becauseFEEandFCSare disjoint)
<PrAjMEECPrAjMCS(by (16.18) and (16.19))
DPrAjMEE[MCS(becauseFEEandFCSare disjoint)so
Pr
AjFEE[FCS<PrAjMEE[MCS;
which directly contradicts the university’s position (16.20)!
But the judge is mistaken; an example where the plaintiff and defence assertions
are all true appears in Section 16.5.8. What is the mistake in the judge’s proof?