STAT 408
Examples for 01/26/2009
Spring 2009
3.
Suppose S =
{
0, 1, 2, 3, …
}
and
P(
0
) =
p
,
P(
k
) =
!
2
1
k
k
⋅
,
k
= 1, 2, 3, … .
Find the value of
p
that would make this a valid probability model.
Must have
∑
∞
=
⋅
+
1
!
2
1
k
k
k
p
= 1.
Since
a
k
k
e
k
a
0
!
=
∑
∞
=
,
1
!
2
1
2
1
1

=
∑
∞
=
⋅
e
k
k
k
.
Therefore,
p
+ (
1
2
1

e
) = 1
and
p
=
2
1
2
e

.
4.
The probability that a randomly selected student at Anytown College owns
a bicycle is 0.55, the probability that a student owns a car is 0.30, and the
probability that a student owns both is 0.10.
P( B ) = 0.55,
P( C ) = 0.30,
P( B
∩
C ) = 0.10.
C
C
'
B
0.10
0.45
0.55
B
'
0.20
0.25
0.45
a)
What is the probability that
a student selected at random
does not own a bicycle?
P( B
'
) = 1 – P( B ) = 1 – 0.55 =
0.45
.
0.30
0.70
1.00
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What is the probability that a student selected at random owns either a car or
a bicycle, or both?
P( B
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 Spring '10
 Mxcon
 Probability, Randomness, Automobile, Potato, potato chips, Bicycle

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