Math 361, Problem set 3
Due 9/20/10
1. (1.4.21) Suppose a fair 6sided die is rolled 6 independent times. A match
occurs if side
i
is observed during the
i
th trial,
i
=1
, . . . ,
6.
(a) What is the probability of at least one match during on the 6 rolls.
(b) Extend part (
a
) to a fair
n
sided die with
n
independent rolls. Then
determine the limit of the probability as
n
→∞
.
2. (1.4.32) Hunters
A
and
B
shoot at a target; their probabilities of hitting
the target are
p
1
and
p
2
respectively. Assuming independent, can
p
1
and
p
2
be chosen so that
P
(0 hits) =
P
(1 hit) =
P
(2 hits)?
3. (1.5.1) Let a card be selected from an ordinary deck of playing cards.
The outcome
c
is one of these 52 cards. Let
X
(
c
) = 4 if
c
is an ace, let
X
(
c
) = 3 if
c
is a king,
X
(
c
) = 2 if
c
is a king and
X
(
c
) = 1 if
c
is
a jack. Otherwise
X
(
c
) = 0. Suppose
P
assigns a probability of
1
52
to
each outcome
c
. Describe the induced probability
P
X
(
D
) on the space
D
=
{
0
,
1
,
2
,
3
,
4
}
of the random variable
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 Fall '10
 Dr.PaulHorn
 probability PX, fair 6sided die, fair nsided die

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