How many balls?

Probability Level 2

One ball is drawn from a box containing 3 red, 2 blue and x x green balls. Find the value of x x so that the probability of drawing a green ball is double that of red or blue ball.


The answer is 10.

Yash Jain by Yash Jain , 21, India

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1 solution

Yash Jain
Mar 18, 2016

Total number of balls ⇒ 3 + 2 + x \Rightarrow 3+2+x

x 3 + 2 + x = 2 ( 3 3 + 2 + x + 2 3 + 2 + x ) \frac{x}{3+2+x} = 2(\frac{3}{3+2+x} + \frac{2}{3+2+x})

x 3 + 2 + x = 2 ( 5 3 + 2 + x ) \frac{x}{3+2+x} = 2(\frac{5}{3+2+x})

x = 2 × 5 x = 2 \times 5

x ⇒ 10 x \Rightarrow \boxed{10}

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