16.7. The Birthday Principle 571
(e)Show that the event that Sally Smart attends MITisindependent of the event
that she is happy.
Class Problems
Problem 16.23.
LetA;B;Cbe events. For each of the following statements, prove it or give a
counterexample.
(a)IfAis independent ofB, andAis independent ofC, thenAis independent of
B\C.
(b)IfAis independent ofB, andAis independent ofC, thenAis independent of
B[C.
(c)IfAis independent ofB, andAis independent ofC, andAis independent of
B\C, thenAis independent ofB[C.
Problem 16.24.
Suppose that you flip three fair, mutually independent coins. Define the following
events:
LetAbe the event thatthe firstcoin is heads. LetBbe the event thatthe secondcoin is heads. LetCbe the event thatthe thirdcoin is heads. LetDbe the event thatan even number ofcoins are heads.(a)Use the four step method to determine the probability space for this experiment
and the probability of each ofA;B;C;D.
(b)Show that these events are not mutually independent.(c)Show that they are 3-way independent.Homework Problems
Problem 16.25.
Define the eventsA;FEE;FCS;MEE, andMCSas 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