Chapter 17 Conditional Probability736
(d)Show that the event that Sally attends Yaleis notindependent of the event that
she is happy.
(e)Show that the event that Sally attends MITisindependent of the event that she
is happy.
Homework Problems
Problem 17.27.
Define the eventsA;FEE;FCS;MEE, andMCSas in Section 17.6.
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,
PrAjFEE<PrAjMEEand (17.13)
PrAjFCS<PrAjMCS: (17.14)
The university’s defence attorneys retort thatoverall, a woman applicant ismore
likely to be granted tenure than a man, namely, that
PrAjFEE[FCS>PrAjMEE[MCS: (17.15)
The judge then interrupts the trial and calls the plaintiff and defence 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:
PrAjFEE[FCSDPrAjFEECPrAjFCS(becauseFEEandFCSare disjoint)
<PrAjMEECPrAjMCS(by (17.13) and (17.14))
DPrAjMEE[MCS(becauseFEEandFCSare disjoint)so
Pr
AjFEE[FCS<PrAjMEE[MCS;
which directly contradicts the university’s position (17.15)!
But the judge is mistaken; an example where the plaintiff and defence assertions
are all true appears in Section 17.6. What is the mistake in the judge’s proof?
Problem 17.28.
It is possible to have three eventsA,B, andCthat: