Chapter 16 Events and Probability Spaces566
events
RWWDRed deck is in the box;
BWWDBlue deck is in the box;
EWWDEight of hearts is picked from the deck in the box:(a)State an inequality between probabilities and/or conditional probabilities that
formalizes the assertion, “picking the eight of hearts from the red deck is more
likely than from the blue deck.”
(b)State a similar inequality that formalizes the assertion “picking the eight of
hearts from the deck in the box makes the red deck more likely to be in the box
than the blue deck.”
(c)Assuming the each deck is equally likely to be the one in the box, prove that
the inequality of part (a) implies the inequality of part (b).
(d)Suppose you couldn’t be sure that the red deck and blue deck were equally
likely to be in the box. Could you still conclude that picking the eight of hearts
from the deck in the box makes the red deck more likely to be in the box than the
blue deck? Briefly explain.
Practice Problems
Problem 16.14.
Dirty Harry places two bullets in the six-shell cylinder of his revolver. He gives the
cylinder a random spin and says “Feeling lucky?” as he holds the gun against your
heart.
(a)What is the probability that you will get shot if he pulls the trigger?(b)Suppose he pulls the trigger and you don’t get shot. What is the probability
that you will get shot if he pulls the trigger a second time?
(c)Suppose you noticed that he placed the two shells next to each other in the
cylinder. How does this change the answers to the previous two questions?
Class Problems
Problem 16.15.
There are two decks of cards. One is complete, but the other is missing the ace
of spades. Suppose you pick one of the two decks with equal probability and then
select a card from that deck uniformly at random. What is the probability that you