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Joint Entrance Examination
Mathematics
Probability
Question 205
Question 205 of 417
Medium
MCQ
E
1
,
E
2
,
E
3
E_1,E_2,E_3
E
1
,
E
2
,
E
3
pairwise independent,
P
(
E
1
)
>
0
P(E_1)>0
P
(
E
1
)
>
0
,
P
(
E
1
∩
E
2
∩
E
3
)
=
0
P(E_1\cap E_2\cap E_3)=0
P
(
E
1
∩
E
2
∩
E
3
)
=
0
. Find
P
(
E
2
c
∩
E
3
c
∣
E
1
)
P(E_2^c\cap E_3^c\mid E_1)
P
(
E
2
c
∩
E
3
c
∣
E
1
)
.
A
P
(
E
2
c
)
+
P
(
E
3
)
P(E_2^c)+P(E_3)
P
(
E
2
c
)
+
P
(
E
3
)
B
P
(
E
3
c
)
−
P
(
E
2
c
)
P(E_3^c)-P(E_2^c)
P
(
E
3
c
)
−
P
(
E
2
c
)
C
P
(
E
3
)
−
P
(
E
2
c
)
P(E_3)-P(E_2^c)
P
(
E
3
)
−
P
(
E
2
c
)
D
P
(
E
3
c
)
−
P
(
E
2
)
P(E_3^c)-P(E_2)
P
(
E
3
c
)
−
P
(
E
2
)
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Official solution
\[P(E_2^c\cap E_3^c\mid E_1) = \frac{P(E_1)-P(E_1\cap(E_2\cup E_3))}{P(E_1)} = 1-P(E_2)-P(E_3) = P(E_3^c)-P(E_2)\]
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