A box contains 24 marbles, some are green and others are blue, if a marble is drawn at random from the box, the probablity that it is green is `2//3`. The number of blue balls in the box is

Options

A. a. 13
B. b. 12
C. c. 16
D. d. 0.08

Answer

To solve the problem step by step, we will follow these instructions:

### Step 1: Understand the problem
We know that there are 24 marbles in total, and the probability of drawing a green marble is given as \( \frac{2}{3} \).

### Step 2: Set up the equation
Let the number of green marbles be \( x \). Since the total number of marbles is 24, the number of blue marbles will be \( 24 - x \).

### Step 3: Write the probability equation
The probability of drawing a green marble can be expressed as:
\[ \text{Probability of green marble} = \frac{\text{Number of green marbles}}{\text{Total number of marbles}} = \frac{x}{24} \]
According to the problem, this probability is equal to \( \frac{2}{3} \). Therefore, we can set up the equation:
\[ \frac{x}{24} = \frac{2}{3} \]

### Step 4: Solve for \( x \)
To solve for \( x \), we can cross-multiply:
\[ 3x = 2 \times 24 \]
\[ 3x = 48 \]
Now, divide both sides by 3:
\[ x = \frac{48}{3} = 16 \]

### Step 5: Find the number of blue marbles
Now that we know the number of green marbles is 16, we can find the number of blue marbles:
\[ \text{Number of blue marbles} = 24 - x = 24 - 16 = 8 \]

### Final Answer
The number of blue marbles in the box is **8**.

---