1
You visited us
1
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard XII
Mathematics
Probability Distribution
Given two ind...
Question
Given two independent events A and B such that P(A)=0.3, P(B)=0.6, Find .
P
(
A
a
n
d
B
)
P
(
A
a
n
d
n
o
t
B
)
P
(
A
o
r
B
)
P
(
n
e
i
t
h
e
r
A
n
o
r
B
)
Open in App
Solution
Given P(A) = 0.3, P (B) = 0.6.
(i): Finding P (A and B):
If A and B are independent events,
P
(
A
∩
B
)
=
P
(
A
)
P
(
B
)
P(A∩B)=P(A)P(B)
⇒
⇒
P
(
A
∩
B
)
=
P
(
A
)
P
(
B
)
P(A∩B)=P(A)P(B)
= 0.3
×
×
0.6 = 0.18
(ii): Finding P (A and not B):
If A and B are independent events,
A
¯
A¯
and
B
¯
B¯
are also independent.
⇒
P
(
A
∩
B
¯
)
=
P
(
A
)
×
P
(
B
¯
)
=
P
(
A
)
×
(
1
−
P
(
B
)
)
=
0.3
×
(
1
−
0.6
)
=
0.3
×
0.4
=
0.12
⇒P(A∩B¯)=P(A)×P(B¯)=P(A)×(1−P(B))=0.3×(1−0.6)=0.3×0.4=0.12
(iii): Finding P (A or B):
P (A
∪
∪
B) = P(A) + P(B) - P(A
∩
∩
B)
⇒
P
(
A
∪
B
)
=
0.3
+
0.6
−
0.18
=
0.72.
⇒P(A∪B)=0.3+0.6−0.18=0.72.
(iv): Finding P (neither A nor B):
P (neither A nor B) = P (
A
¯
∩
B
¯
A¯∩B¯
) = 1 - P (A
∪
∪
B) = 1 - 0.72 = 0.28.
Suggest Corrections
0
Similar questions
Q.
Given two independent events
A
and
B
such that
P
(
A
)
=
0.3
,
P
(
B
)
=
0.6
. Find
(i)
P
(
A
a
n
d
B
)
(ii)
P
(
A
a
n
d
n
o
t
B
)
(iii)
P
(
A
o
r
B
)
(iv)
P
(
n
e
i
t
h
e
r
A
n
o
r
B
)
If the sum of the above probablities is
m
enter
100
m
Q.
Given two independent events
A
,
B
such that
P
(
A
)
=
0.3
,
P
(
B
)
=
0.6
. Determine
P
(
A
a
n
d
n
o
t
B
)
Q.
Given two independent events
A
,
B
such that
P
(
A
)
=
0.3
,
P
(
B
)
=
0.6
. Determine
P
(
A
a
n
d
B
)
Q.
Given two independent events A and B such that P(A) = 0.3, P(B) = 0.6 Find
P(A and B)
Q.
Given two independent events A and B such that
P
(
A
)
=
0.3
,
P
(
B
)
=
0.6
then, find
P
(
A
∩
B
)
View More
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
Related Videos
Probability Distribution
MATHEMATICS
Watch in App
Explore more
Probability Distribution
Standard XII Mathematics
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
AI Tutor
Textbooks
Question Papers
Install app