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NCERT Class XII Mathematics Chapter - - Solutions

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Question : 47
Total: 101
A card from a pack of 52 cards is lost. From the remaining cards of the pack, two cards are drawn and are found to be both diamonds. Find the probability of the lost card being a diamond.
Solution:  
Let E1 : ‘lost card is a diamond’, E2 : ‘lost card is not a diamond’,
⇒P(E1)=
13
52
=
1
4
 and P(E2)=
39
52
=
3
4
Let A : ‘two cards drawn from the remaining pack are diamonds’,
Then, P(A|E1)=
12C2
51C2
=
12×11
51×50
 and P(A|E2)=
13C2
51C2
=
13×12
51×50
∴ Required probability,
=P(E1|A)=
P(A|E1)P(E1)
P(A|E1)P(E1)+P(A|E2)P(E2)
=
12×11
51×50
×
1
4
12×11
51×50
×
1
4
+
13×12
51×50
×
3
4
=
11
50
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