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Byju's Answer
Standard XII
Mathematics
Intersection of Sets
If the events...
Question
If the events
A
and
B
are independent and if
P
(
¯
¯¯
¯
A
)
=
2
3
,
P
(
¯
¯¯
¯
B
)
=
2
7
, then
P
(
A
∩
B
)
is equal to
A
4
21
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B
3
21
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C
5
21
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D
2
21
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E
1
21
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Solution
The correct option is
C
5
21
Given,
P
(
¯
¯¯
¯
A
)
=
2
3
Therefore,
P
(
A
)
=
1
−
P
(
¯
¯¯
¯
A
)
=
1
−
2
3
=
1
3
and
P
(
¯
¯¯
¯
B
)
=
2
7
∴
P
(
B
)
=
1
−
P
(
¯
¯¯
¯
B
)
=
1
−
2
7
=
5
7
Given,
A
and
B
are independent events.
Thus
P
(
A
∩
B
)
=
P
(
A
)
⋅
P
(
B
)
=
1
3
⋅
5
7
=
5
21
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0
Similar questions
Q.
If the events A and B are independent if
P
(
A
′
)
=
2
3
and
P
(
B
′
)
=
2
7
, then
P
(
A
∩
B
)
is equal to.
Q.
If the events A and B are such that
P
(
A
)
=
1
4
,
P
(
A
B
)
=
1
2
and
P
(
B
A
)
=
2
3
, the P(B) is equal to
Q.
If
A
=
⎡
⎢
⎣
0
1
2
1
2
3
3
a
1
⎤
⎥
⎦
and
A
−
1
=
⎡
⎢
⎣
1
/
2
1
/
2
1
/
2
−
4
3
c
5
/
2
−
3
/
2
1
/
2
⎤
⎥
⎦
, then the values of
a
and
c
are equal to
Q.
If A & B are independent events such that
P
(
B
)
=
2
7
,
P
(
A
∪
¯
¯¯
¯
B
)
=
0.8
, then
P
(
A
)
is equal to
Q.
If
A
=
⎡
⎢
⎣
0
1
2
1
2
3
3
a
1
⎤
⎥
⎦
and
A
−
1
=
⎡
⎢
⎣
1
/
2
1
/
2
1
/
2
−
4
3
c
5
/
2
−
3
/
2
1
/
2
⎤
⎥
⎦
then the values of
a
and
c
are equal to
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