A box contains $$(12 + x)$$ red balls and $$(18 + x)$$ green balls. A ball is drawn at random and is found to be red. If the probability of the drawn ball being red is $$\frac{5}{12}$$, find the value of $$x$$.

Question

Accepted Answer

1. **Understand the probability formula**:  
   The probability of an event is given by:  
   $$
   P(	ext{Red Ball}) = \frac{	ext{Number of Red Balls}}{	ext{Total Number of Balls}}
   $$

2. **Substitute the given values**:  
   - Number of red balls = $$12 + x$$.  
   - Total number of balls = $$(12 + x) + (18 + x) = 30 + 2x$$.  
   - Probability of drawing a red ball = $$\frac{5}{12}$$.

Using the formula:  
   $$
   \frac{5}{12} = \frac{12 + x}{30 + 2x}
   $$

3. **Simplify the equation**:  
   Cross-multiply to eliminate the fraction:  
   $$
   5(30 + 2x) = 12(12 + x)
   $$  
   Expand both sides:  
   $$
   150 + 10x = 144 + 12x
   $$  
   Simplify to isolate $$x$$:  
   $$
   150 - 144 = 12x - 10x
   $$  
   $$
   6 = 2x
   $$  
   $$
   x = 3
   $$

4. **Verify the solution**:  
   Substitute $$x = 3$$ back into the probability formula:  
   - Number of red balls = $$12 + 3 = 15$$.  
   - Total number of balls = $$30 + 2(3) = 36$$.  
   - Probability = $$\frac{15}{36} = \frac{5}{12}$$, which matches the given probability.

Thus, the correct answer is **(b) 3**.

Answer

Answer

Answer