Question

A bag contains 5 red balls and some blue balls. The probability of drawing a blue ball is double that of a red ball. What is the number of blue balls in the bag?

• A. 8
• B. 10
• C. 9
• D. 7

Answer 1

The correct option is B 10

Let the number of blue balls be $x$.
Total number of balls = $x+5$.
Probability of drawing a red ball, $P\left(r\right)$ = $\frac{5}{x+5}$
Probability of drawing a blue ball, $P\left(b\right)$ = $\frac{x}{x+5}$
(See that $P\left(r\right)=1-P\left(b\right)$)
According the question,
$P\left(b\right)=2\times P\left(r\right)$
$\Rightarrow$$\frac{x}{x+5}=2\times \frac{5}{x+5}$
$\Rightarrow$ $x=2\times 5=10$
$\therefore$ number of blue balls = 10.