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Joint Entrance Examination
Mathematics
Probability
Question 254
Question 254 of 417
Medium
MCQ
X
∼
B
(
n
,
p
)
X\sim B(n,p)
X
∼
B
(
n
,
p
)
,
P
(
X
=
2
)
=
P
(
X
=
3
)
P(X=2)=P(X=3)
P
(
X
=
2
)
=
P
(
X
=
3
)
. Find
E
(
X
)
E(X)
E
(
X
)
.
A
2
−
p
2-p
2
−
p
B
3
−
p
3-p
3
−
p
C
p
2
p^2
p
2
D
p
3
p^3
p
3
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Official solution
n
C
2
p
2
q
n
−
2
=
n
C
3
p
3
q
n
−
3
⇒
1
n
−
2
=
p
3
q
⇒
n
p
=
3
−
p
{}^nC_2p^2q^{n-2}={}^nC_3p^3q^{n-3} \Rightarrow \dfrac{1}{n-2}=\dfrac{p}{3q}\Rightarrow np=3-p
n
C
2
p
2
q
n
−
2
=
n
C
3
p
3
q
n
−
3
⇒
n
−
2
1
=
3
q
p
⇒
n
p
=
3
−
p
.
E
(
X
)
=
n
p
=
3
−
p
E(X)=np=3-p
E
(
X
)
=
n
p
=
3
−
p
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