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CBSE Class 12 Maths 2010 Solved Paper

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Question : 25
Total: 29
A card form a pack of 52 cards is lost. From the remaining cards of the pack, two cards are drawn at random and are found to be both clubs. Find the probability of the lost card being of clubs.
OR
From a lot of 10 bulbs, which includes 3 defectives, a sample of 2 bulbs is drawn at random. Find the probability distribution of the number of defective bulbs.
Solution:  
Let the events E1,E2,E3,E4 and A be defined as follows:
E1: Missing card is a diamond
E2: Missing card is a spade
E3: Missing card is a club
E4: Missing card is a heart
A: Drawing two club cards
P (E1) = P (E2) = P (E3) = P (E4) =
1
4
P (A|E3) =
12
51
×
11
50
P (E3|A) =
4
Σ
i=1
P(E3)P(A|E3)
P(E1)P(A|E1)
=
1
4
×
12
51
×
11
50
1
4
[
3×12+13×12+13×12+11×12
51×50
]

=
12×11
3×13×12+12×11
 =
11
50
OR
Total number of bulbs = 10
Number of defective bulbs = 3
Number of non-defective bulbs = 7
P(drawing a defective bulb), p =
3
10
P(drawing a non-defective bulb), q =
7
10
Two bulbs are drawn.
Let X denote the number of defective bulbs, then X can take values 0, 1, and 2.
P(X = 0) = P(drawing both non-defective bulbs) = (
7
10
)2
P(X = 1) = P(drawing one defective and one non defective bulb)
= P (drawing a non-defective bulb and a defective bulb) + P (drawing a defective bulb and a non - effective bulb)
= (
7
10
)(
3
10
) + (
3
10
)(
7
10
) =
21
50
P(X = 2) = P(drawing both defective bulbs)= (
3
10
)2
Required probability distribution is
X 0 1 2
P (X)
49
100
51
50
9
100
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