Question

A bag contains $6$red, $5$white and $4$black balls. Two balls are drawn. The probability that none of them is red, is

• A. $\frac{12}{35}$
• B. $\frac{6}{35}$
• C. $\frac{4}{35}$
• D. None of these

Answer 1

The correct option is A

$\frac{12}{35}$

Explanation for correct option:

Calculate the Probability :

Total number of balls $=6+5+4=15$

If two balls are drawn, then the total number of cases $={}^{15}C_2$

The number of cases that, none of the balls are red (5 white + 4 black) $={}^9{C}_2$

$\mathbf{Probability}\mathbf{}\mathbf{=}\frac{\mathbf{Fovourable}\mathbf{}\mathbf{cases}}{\mathbf{Total}\mathbf{}\mathbf{cases}}$

$=\frac{{}^{9}C_2}{{}^{15}C_2}$

$=\frac{36}{105}=\frac{12}{35}$

Hence the correct option is (A).