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Mathematics
Mathematics
Problem
Let
A
A
A
and
B
B
B
be the two events of a sample space
S
S
S
and let
E
E
E
be an event such that
P
(
E
)
≠
0
P(E) \neq 0
P
(
E
)
=
0
. Then, prove that
P
[
(
A
∪
B
)
/
E
]
=
P
(
A
/
E
)
+
P
(
B
/
E
)
−
P
[
(
A
∩
B
)
/
E
]
.
P[(A \cup B)/E] = P(A/E) + P(B/E) - P[(A \cap B)/E].
P
[(
A
∪
B
)
/
E
]
=
P
(
A
/
E
)
+
P
(
B
/
E
)
−
P
[(
A
∩
B
)
/
E
]
.
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