Mathematics for Computer Science

17.8. Mutual Independence 733

The guard will truthfully tell Voldemort the name of one of the prisoners to be
released. We’re interested in the following events:

V:Voldemort is released.

“F”: The guard tells Voldemort thatFoo Foo will be released.

“S”: The guard tells Voldemort thatSauron will be released.

The guard has two rules for choosing whom he names:

 never say that Voldemort will be released,

 if both Foo Foo and Sauron are getting released, say “Foo Foo.”

(b)What is Pr



V j“F”



?

(c)What is Pr



V j“S”



?

(d)Show how to use the Law of Total Probability to combine your answers to
parts (b) and (c) to verify that the result matches the answer to part (a).

Problems for Section 17.8

Practice Problems

Problem 17.22.
SupposeA,B, andC are mutually independent events, what aboutA\Band
B[C?

Class Problems

Problem 17.23.
Suppose 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.