In a box there are 6 blue ball, X red balls & 10 green balls. Probability of choosing one red ball from the given box is 1/3, then find the sum of red and blue balls in the box?

Options

A. `14`
B. `11`
C. `10`
D. `17`

Answer

To solve the problem step by step, we need to find the number of red balls (X) in the box and then calculate the sum of red and blue balls.

### Step 1: Understand the given data
We know that:
- Number of blue balls = 6
- Number of red balls = X
- Number of green balls = 10
- Total probability of choosing one red ball = 1/3

### Step 2: Calculate the total number of balls in the box
The total number of balls in the box can be calculated as:
\[ \text{Total balls} = \text{Number of blue balls} + \text{Number of red balls} + \text{Number of green balls} \]
\[ \text{Total balls} = 6 + X + 10 = X + 16 \]

### Step 3: Set up the probability equation
The probability of choosing one red ball is given by the formula:
\[ \text{Probability of red ball} = \frac{\text{Number of red balls}}{\text{Total number of balls}} \]
Substituting the known values:
\[ \frac{X}{X + 16} = \frac{1}{3} \]

### Step 4: Cross-multiply to solve for X
Cross-multiplying gives us:
\[ 3X = 1(X + 16) \]
Expanding the right side:
\[ 3X = X + 16 \]

### Step 5: Rearrange the equation
Rearranging the equation to isolate X:
\[ 3X - X = 16 \]
\[ 2X = 16 \]

### Step 6: Solve for X
Dividing both sides by 2:
\[ X = 8 \]

### Step 7: Calculate the sum of red and blue balls
Now that we have the number of red balls (X = 8), we can find the sum of red and blue balls:
\[ \text{Sum of red and blue balls} = \text{Number of red balls} + \text{Number of blue balls} \]
\[ \text{Sum} = 8 + 6 = 14 \]

### Final Answer
The sum of red and blue balls in the box is **14**.

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