Question

A bag contains 5 white, 8 red and x green balls. If the probability of drawing a red ball is $\frac{2}{3}$ times the probability of drawing a green ball, then the value of x is equal to

• A. 8
• B. 13
• C. 5
• D. 12

Answer 1

The correct option is D 12

Given that the bag contains 5 white, 8 red and x green balls.
$\therefore \text{Total number of balls}=5+8+x=13+x$


$\text{Probability}=\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}$

$\therefore \text{P(Red ball)}=\frac{8}{13+x}$

$\text{P(Green ball)}=\frac{x}{13+x}$

According to the question:
$\text{P(Red ball)}=\frac{2}{3}\text{P(Green ball)}$
$\Rightarrow \frac{8}{13+x}=\frac{2}{3}\times \frac{x}{13+x}$

$\Rightarrow \frac{2}{3}x=8$

$\Rightarrow x=12$

Hence, the correct answer is option (d).