Question

A bag contains $4$ white, $3$ black and $2$ red balls. Balls are drawn from the bag one by one without replacement.
The probability that the $4^{\text{th}}$ ball is red is

• A. $\frac{1}{16}$
• B. $\frac{1}{9}$
• C. $\frac{2}{9}$
• D. $\frac{3}{11}$

Answer 1

The correct option is C $\frac{2}{9}$

A bag contains $4$ white, $3$ black and $2$ red balls.

$4^{\text{th}}$ ball is red :
Number of ways of choosing the $4^{\text{th}}$ ball $={}^2{C}_1$
Required probability$=\frac{{}^2{C}_1\cdot 8\cdot 7\cdot 6}{9\cdot 8\cdot 7\cdot 6}=\frac{2}{9}$