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Joint Entrance Examination
Mathematics
Probability
Question 21
Question 21 of 417
Medium
MCQ
Bag 1 contains 4 white balls and 5 black balls, and Bag 2 contains n white balls and 3 black balls. One ball is drawn randomly from Bag 1 and transferred to Bag 2. A ball is then drawn randomly from Bag 2. If the probability, that the ball ...
A
5
B
6
C
4
D
3
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Solutions · 1
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Official solution
1
=
4
W
,
5
B
2
=
n
W
,
3
B
P
(
W
B
a
g
2
)
=
29
45
⇒
P
(
W
B
1
)
×
P
(
W
B
2
)
+
P
(
B
B
1
)
×
P
(
W
B
2
)
=
29
45
4
9
×
n
+
1
n
+
4
+
5
9
×
n
n
+
4
=
29
45
\begin{gathered} 1={4W,5B} \\ 2={nW,3B} \\ P(\frac{W}{Bag2})=\frac{29}{45} \\ \Rightarrow P(\frac{W}{{B}_{1}})\times P(\frac{W}{{B}_{2}})+P(\frac{B}{{B}_{1}})\times P(\frac{W}{{B}_{2}})=\frac{29}{45} \\ \frac{4}{9}\times \frac{n+1}{n+4}+\frac{5}{9}\times \frac{n}{n+4}=\frac{29}{45} \end{gathered}
1
=
4
W
,
5
B
2
=
nW
,
3
B
P
(
B
a
g
2
W
)
=
45
29
⇒
P
(
B
1
W
)
×
P
(
B
2
W
)
+
P
(
B
1
B
)
×
P
(
B
2
W
)
=
45
29
9
4
×
n
+
4
n
+
1
+
9
5
×
n
+
4
n
=
45
29
n
=
6
n=6
n
=
6
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