Examples for 01/28/2011
Spring 2011
Events
A
and
B
are
independent
if
and
only
if
P
(
B
A
)
=
P
(
B
)
P
(
A
B
)
=
P
(
A
)
P
(
A
∩
B
)
=
P
(
A
)
⋅
P
(
B
)
1.
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.
Are events {a student owns a bicycle} and {a student owns a car}
independent?
Events
A,
B
and
C
are
independent
if
and
only
if
P
(
A
∩
B
) = P
(
A
)
⋅
P
(
B
),
P
(
A
∩
C
) = P
(
A
)
⋅
P
(
C
),
P
(
B
∩
C
) = P
(
B
)
⋅
P
(
C
),
and
P
(
A
∩
B
∩
C
) = P
(
A
)
⋅
P
(
B
)
⋅
P
(
C
)
2.
A girl is told by her boyfriend that she is “one in a billion.”
She has a dimple
in her chin, probability
1
/
100
,
eyes of different colors, probability
1
1,000
,
and is absolutely crazy about mathematics, probability
1
10,000
b)
Show why the girl is “one in a billion.”
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 Spring '08
 Kim
 Probability, Bart Simpson, Simpsons Roasting on an Open Fire, Springfield Elementary School, Principal Skinner

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