Question

A bag contains $14$ balls of which $\text{x}$ are white . If $6$ more white balls are added to the bag,the probability of drawing a white ball is $\frac{1}{2}$, then $\text{x=}$

Answer 1

Total number of balls $=14$

Number of white balls $=\text{x}$

If $6$ more white balls were added then ,

Total number of balls $=14+6$$=20$

Number of white balls $=\text{x+6}$

Probability of drawing a white ball is $=\frac{1}{2}$

Probability$=\frac{\text{number of white balls}}{\text{total number of balls}}$

$$\begin{gathered} \Rightarrow \frac{\text{x+6}}{20}=\frac{1}{2} \\ \Rightarrow \text{x+6=}\frac{20}{2}\text{=10} \\ \Rightarrow \text{x+6=10} \\ \Rightarrow \text{x=10-6=4} \end{gathered}$$

Hence the number of white balls are $4$.