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NCERT Class XII Mathematics Chapter - - Solutions

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Question : 94
Total: 101
Suppose we have four boxes A, B, C and D containing coloured marbles as given below :
 Box  Marble colour
   Red  White  Black
 A  1  6  3
 B  6  2  2
 C  8  1  1
 D  0  6  4
One of the boxes has been selected at random and a single marble is drawn from it. If the marble is red, what is the probability that it was drawn from box A ?, box B ?, box C ?
Solution:  
Let E1 : box A be selected E2 : box B be selected ; E3 : box C be selected; E4 : box D be selected
A : Red marble be drawn
P(E1)=
1
4
,P(E2)=
1
4
, P(E3)=
1
4
,P(E4)=
1
4

P(A|E1)=
1
10
,P(A|E2)=
6
10
 , P(A|E3)=
8
10
,P(A|E4)=
0
10
P(E1|A)=
P(E1)P(A|E1)
P(E1)P(A|E1)+P(E2)P(A|E2)+P(E3)P(A|E3)+P(E4)P(A|E4)
=
(
1
4
×
1
10
)
(
1
4
×
1
10
+
1
4
×
6
10
+
1
4
×
8
10
+
1
4
×
0
10
)
=
1
15
P(E2|A)=
P(E2)P(A|E2)
P(E1)P(A|E1)+P(E2)P(A|E2)+P(E3)P(A|E3)+P(E4)P(A|E4)
=
(
1
4
×
6
10
)
(
1
4
×
1
10
+
1
4
×
6
10
+
1
4
×
8
10
+
1
4
×
0
10
)
=
2
5
P(E3|A)=
P(E3)P(A|E3)
P(E1)P(A|E1)+P(E2)P(A|E2)+P(E3)P(A|E3)+P(E4)P(A|E4)
=
(
1
4
×
8
10
)
(
1
4
×
1
10
+
1
4
×
6
10
+
1
4
×
8
10
+
1
4
×
0
10
)
=
8
15
So, P(E1|A)=
1
15
, P(E2|A)=
2
5
, P(E3|A)=
8
15
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