Question

Three balls are drawn at random without replacement from a box containing 2 white, 3 red and 4 black balls. If X denotes the number of white balls drawn and Y denotes the number of red balls drawn, find P(x=1,Y=2). *

1/21

2/21

1/14

3/14​

Answer 1

Given :

No. of white balls = 2

No. of red balls = 3

No. of black balls = 4

Balls drawn without replacement = 3

To find :

P(X = 1 , Y = 2)

where X = no. of white balls drawn

Y = no. of red balls drawn

Solution :

Total no. of balls = 2 + 3 + 4 = 9

P(X = 1 , Y = 2) = ²C₁ * ³C₂

                               ⁹C₃

P(X = 1 , Y = 2) = ( 2! / 1! × 1!) × (3! / 2! × 1!)

                                    (9! / 3! × 6!)

P(X = 1 , Y = 2) =   2 × 3    

                           9 × 8 × 7

                             3 × 2

P(X = 1 , Y = 2) = 1/14