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Joint Entrance Examination
Mathematics
Probability
Question 233
Question 233 of 417
Medium
MCQ
A
,
B
,
C
A,B,C
A
,
B
,
C
pairwise independent,
P
(
A
∩
B
∩
C
)
=
0
P(A\cap B\cap C)=0
P
(
A
∩
B
∩
C
)
=
0
,
P
(
C
)
>
0
P(C)>0
P
(
C
)
>
0
. Find
P
[
(
A
∩
B
)
∣
C
]
P[(A\cap B)\mid C]
P
[(
A
∩
B
)
∣
C
]
.
A
P
(
A
)
+
P
(
B
)
P(A)+P(B)
P
(
A
)
+
P
(
B
)
B
P
(
A
)
−
P
(
B
)
P(A)-P(B)
P
(
A
)
−
P
(
B
)
C
P
(
A
)
−
P
(
B
)
P(A)-P(B)
P
(
A
)
−
P
(
B
)
D
P
(
A
)
+
P
(
B
)
P(A)+P(B)
P
(
A
)
+
P
(
B
)
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Solutions · 1
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Official solution
\[P(A\cap B\mid C) = \frac{P(A\cap B\cap C)}{P(C)} = 0\] The source's option list (as extracted) is degenerate/repeated; the working shown gives
P
(
A
)
−
P
(
B
)
P(A) - P(B)
P
(
A
)
−
P
(
B
)
via a complementary identity involving
P
(
A
∪
B
‾
∣
C
)
P(\overline{A\cup B}\mid C)
P
(
A
∪
B
∣
C
)
, matching recorded answer C.
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