Question

A bag contains $10$ white balls and $X$ black balls. If probability of drawing white balls is double that black ball then answer the following: What is the probability of drawing a black ball

• A. $\frac{7}{3}$
• B. $\frac{2}{3}$
• C. $\frac{1}{3}$
• D. $\frac{5}{6}$

Answer 1

The correct option is B $\frac{2}{3}$

Total no. of balls $=10+X$

Probability of drawing black ball $=\frac{X}{10+X}$

Probability of drawing white ball $=\frac{10}{10+X}$

Given that the probability of drawing white balls is double that of black ball

$\therefore \frac{X}{10+X}=2\left(\frac{10}{10+X}\right)$

$\therefore \frac{X}{10+X}=\left(\frac{20}{10+X}\right)$

$\therefore X=20$

Probability of drawing black ball $=$ $\frac{X}{10+X}=\frac{20}{30}=\frac{2}{3}$