Question

If from each of the three boxes containing 3 white and 1 black, 2 white and 2 black, 1 white and 3 black balls, one ball is drawn at random, then the probability that 2 white and 1 black balls will be drawn, is A. 13 32 B. 1 4 C. 1 32 D. 3 16 Select the correct answer from above options

Answer 1

---

Correct Answer - A

The contents of three boxes are

I

3

W

1

B

I

I

2

W

2

B

I

I

I

1

W

3

B

I

Let

W

i

(

i

=

1

,

2

,

3

)

W

be the event of drawing a white ball from ith box and

B

i

(

i

=

1

,

2

,

3

)

B

be the event of drawing a black ball from ith box. Then,

Required probability

=

P

(

W

1

∩

W

2

∩

B

3

)

∪

(

W

1

∩

B

2

∩

W

3

)

(

B

1

∩

W

2

∩

W

3

)

=

=

P

(

W

1

∩

W

2

∩

B

3

+

P

(

W

1

∩

B

2

∩

W

3

)

+

P

(

B

1

∩

W

2

∩

W

3

)

=

=

P

(

W

1

)

P

(

W

2

)

P

(

B

3

)

+

P

(

W

1

)

P

(

B

2

)

P

(

W

3

)

+

P

(

B

1

)

P

(

W

2

)

P

(

W

3

)

=

=

3

4

×

2

4

×

3

4

+

3

4

×

2

4

×

1

4

+

1

4

×

2

4

×

1

4

=

26

64

=

13

32

=