Which of the following is incorect?
b) 0<=P(A) <=1
d) P(A) + P(A) =1
a) P(A)>1
Answers
Answered by
4
Correct option is
B
A and
B
ˉ
are independent
C
A
ˉ
,
B
ˉ
are independent
D
P(A/B)+P(
A
ˉ
/B)=1
If A and B are independent then P(A∩B)=P(A)P(B)
nowP(A∩
B
)=P(A)−P(A∩B)=P(A)−P(A)P(B)
=P(A){1−P(B)}=P(A)P(
B
)
Hence A and
B
are independent.
similarly P(
A
∩
B
)=1−P(A∪B)=1−P(A)−P(B)+P(A∩B)
=1−P(A)−P(B)+P(A)P(B)=1−P(A)−P(B){1−P(A)}
={1−P(A)}{1−P(B)}=P(
A
)P(
B
)
Hence
A
and
B
are independent.
and P(A/B)+P(
A
/B)=
P(B)
P(A∩B)
+
P(B)
P(
A
∩B)
=
P(B)
P(A)P(B)+P(
A
)P(B)
=P(A)+P(
A
)=1
Option A is incorrect because P(A∩B)=P(A)P(B)
=0 since A/Q P(A)>0andP(B)>0
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