Question

A bag contains $15$ balls of which $x$ are black are remaining are red. If the number of red balls are increased by $5$, the probability of drawing the red balls doubles, then the probability of drawing red ball, then the probability of drawing red ball is _______.

• A. $\frac{1}{5}$
• B. $\frac{4}{5}$
• C. $\frac{3}{5}$
• D. $\frac{2}{5}$

Answer 1

The correct option is A $\frac{1}{5}$

Total number of balls (both red and black) $=15$

Number of black balls $=x$

Number of red balls $=15-x$

Probability of drawing a red ball $=\frac{15-x}{15}$

After adding $5$ more red balls,

Probability of drawing a red ball $=\frac{20-x}{20}$

It is given that $\frac{20-x}{20}=2\left(\frac{15-x}{15}\right)$

On solving, we get $x=12$

So, Probability of drawing a red ball $=\frac{15-x}{15}=\frac{1}{5}$