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Byju's Answer
Standard XII
Mathematics
Intersection of Sets
A and B are...
Question
A
and
B
are two independent events of an experiment .if
P
(
n
o
t
B
)
=
0.65
,
P
(
A
∪
B
)
=
0.85
,find
P
(
A
)
.
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Solution
P
(
¯
B
)
=
0.65
⇒
P
(
¯
B
)
=
1
−
P
(
B
)
=
0.65
⇒
P
(
B
)
=
0.35
,
P
(
A
∪
B
)
=
0.85
now,
P
(
A
∪
B
)
=
P
(
A
)
+
P
(
B
)
−
P
(
A
∩
B
)
since
A
,
B
are independent events.
⇒
0.85
=
P
(
A
)
+
0.35
−
P
(
A
)
(
0.35
)
∴
0.50
=
0.65
P
(
A
)
⇒
P
(
A
)
=
0.50
0.65
=
10
13
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Similar questions
Q.
If P (not B) = 0.65, P (A ∪ B) = 0.85, and A and B are independent events, then find P (A).
Q.
If P(B')=0.65,
P
(
A
∪
B
)
=
0.85
and A and B are independent events, then find P(A).
Q.
If A and B are two events associated with a random experiment for which
P
(
A
)
=
0.35
,
P
(A or B)
=
0.85
,
and P(A and B)
=
0.15.
Find P(only B).
Q.
If
P
(
¯
A
)
=
0.65
,
P
(
A
∪
B
)
=
0.65
,
where A and B are two mutually exclusive events. then find P(B).
Q.
If A and B are independent events of a random experiment such that
P
(
A
∩
B
)
=
1
6
and
P
(
¯
¯¯
¯
A
∩
¯
¯¯
¯
B
)
=
1
3
, then
P
(
A
)
is equal to
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