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Joint Entrance Examination
Mathematics
Probability
Question 265
Question 265 of 417
Medium
MCQ
A
,
B
,
C
A,B,C
A
,
B
,
C
pairwise independent,
P
(
C
)
>
0
P(C)>0
P
(
C
)
>
0
,
P
(
A
∩
B
∩
C
)
=
0
P(A\cap B\cap C)=0
P
(
A
∩
B
∩
C
)
=
0
. Find
P
(
A
c
∩
B
c
∣
C
)
P(A^c\cap B^c\mid C)
P
(
A
c
∩
B
c
∣
C
)
.
A
P
(
B
c
)
−
P
(
B
)
P(B^c)-P(B)
P
(
B
c
)
−
P
(
B
)
B
P
(
A
c
)
+
P
(
B
c
)
P(A^c)+P(B^c)
P
(
A
c
)
+
P
(
B
c
)
C
P
(
A
c
)
−
P
(
B
c
)
P(A^c)-P(B^c)
P
(
A
c
)
−
P
(
B
c
)
D
P
(
A
c
)
−
P
(
B
)
P(A^c)-P(B)
P
(
A
c
)
−
P
(
B
)
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Official solution
\[P(A^c\cap B^c\mid C) = \frac{P(C)-P(A\cap C)-P(B\cap C)+P(A\cap B\cap C)}{P(C)} = 1-P(A)-P(B) = P(A^c)-P(B)\]
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