A box contains \((12+x)\) red balls and \((18+x)\) green balls. A ball is drawn at random. If the probability of drawing a red ball is \(\frac{5}{12}\), then find the value of \(x\).
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 3
The probability of drawing a red ball = (number of red balls) ÷ (total number of balls); this is set equal to \(\frac{5}{12}\).
Total number of balls in the box: \((12+x)+(18+x)=30+2x\)
Red balls over all the balls equals the given probability: \(\displaystyle \frac{12+x}{30+2x}=\frac{5}{12}\)
\(144+12x=150+10x\)
\(2x=6\), so \(x=3\)