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 ball will be drawn is

• A. 13/32
• B. ¼
• C. 1/32
• D. 3/16

Answer 1

Answer: (A)

13/32

Answer 2

The contents of three boxes are

3W 1B

II 2W 2B

III 1W 3B

Let $\mathrm { W } _ { \mathrm { i } } ( \mathrm { i } = 1,2,3 )$ be the event of drawing a white ball from $i ^ { \text {th } }$ box and $\mathrm { B } _ { \mathrm { i } } ( \mathrm { i } = 1,2,3 )$ be the event of drawing a

black ball from 0th box. Then,

Required probability.

$= \mathrm { P } \left( \mathrm { W } _ { 1 } \right) \mathrm { P } \left( \mathrm { W } _ { 2 } \right) \mathrm { P } \left( \mathrm { B } _ { 3 } \right) + \mathrm { P } \left( \mathrm { W } _ { 1 } \right) \mathrm { P } \left( \mathrm { B } _ { 2 } \right) \mathrm { P } \left( \mathrm { W } _ { 3 } \right)$