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Statistics Examples
Step-by-Step Examples
Statistics
Probability
Find P(A∩B) for Dependent Events A and B
P
(
A
)
=
0.2
P
(
A
)
=
0.2
,
P
(
B
)
=
0.09
P
(
B
)
=
0.09
,
P
(
B
g
i
v
e
n
A
)
=
0.03
P
(
B
g
i
v
e
n
A
)
=
0.03
Step 1
When
A
A
and
B
B
are
dependent events
, the
probability
of
A
A
and
B
B
occurring is
P
(
A
∩
B
)
=
P
(
A
)
⋅
(
P
(
B
|
A
)
)
P
(
A
∩
B
)
=
P
(
A
)
⋅
(
P
(
B
|
A
)
)
, which is called the
multiplication
rule for
dependent events
A
A
and
B
B
.
P
(
A
∩
B
)
=
P
(
A
)
⋅
(
P
(
B
|
A
)
)
P
(
A
∩
B
)
=
P
(
A
)
⋅
(
P
(
B
|
A
)
)
Step 2
Fill in the known values.
P
(
A
∩
B
)
=
0.2
⋅
0.03
P
(
A
∩
B
)
=
0.2
⋅
0.03
Step 3
Multiply
0.2
0.2
by
0.03
0.03
.
P
(
A
∩
B
)
=
0.006
P
(
A
∩
B
)
=
0.006
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x
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2
√
π
∫
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x
⎤
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[
x
2
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∫
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]
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