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Mathematics
Problem
Explain, in not more than two sentences, why the expression for
P
(
E
1
∩
E
2
∩
E
3
)
P(E_1\cap E_2\cap E_3)
P
(
E
1
∩
E
2
∩
E
3
)
simplifies to
P
(
E
1
)
P
(
E
2
∣
E
1
)
P
(
E
3
∣
E
1
)
P(E_1)\,P(E_2\mid E_1)\,P(E_3\mid E_1)
P
(
E
1
)
P
(
E
2
∣
E
1
)
P
(
E
3
∣
E
1
)
if
E
2
E_2
E
2
and
E
3
E_3
E
3
are independent given
E
1
E_1
E
1
.
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