University of California, San Diego
ECE109:
Problem Set #2
1.
Find
in each of the following four cases:
(a)
,
, and
are disjoint events and
.
(b)
(c)
,
, and
(d)
2.
Two fair dice are rolled. What is the conditional probability that the two dice show the same
number given that the sum of the two numbers is greater than seven?
3.
Let
and
be events. Show that
. When does equality hold?
4.
Monty Hall, the host of the TV game show “Let’s Make A Deal”, shows you three curtains. One
curtain conceals a valuable prize, while the other two conceal junk. All three curtains are equally
likely to conceal the prize. He offers you the following “deal”: pick a curtain, and you can have
whatever is behind it. When you pick a curtain, instead of giving you what lies behind the curtain,
Monty (who knows where the prize is) opens one of the remaining curtains to show you that there
is junk behind it, and offers the following “new, improved deal”: you can either stick with your
original choice, or switch to the remaining (unopened) curtain. Amidst the deafening roars of
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 Fall '08
 KennethZeger
 Conditional Probability, Probability, Englishlanguage films, monty hall problem, Monty, new improved deal

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