A jar contains 24 marbles, some are green and others are blue. If a marble is drawn at random from the jar, the probability that it is green is 2/3.Find the number of blue marbles in the jar.

Answer

To solve the problem step by step, we can follow these steps:

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

### Step 2: Set up the equation for the probability
The probability of drawing a green marble can be expressed as:
\[ P(\text{Green}) = \frac{\text{Number of Green Marbles}}{\text{Total Number of Marbles}} \]
Given that the total number of marbles is 24, we can write:
\[ P(\text{Green}) = \frac{\text{Number of Green Marbles}}{24} \]
Since we know that \( P(\text{Green}) = \frac{2}{3} \), we can set up the equation:
\[ \frac{\text{Number of Green Marbles}}{24} = \frac{2}{3} \]

### Step 3: Solve for the number of green marbles
To find the number of green marbles, we can cross-multiply:
\[ \text{Number of Green Marbles} = 24 \times \frac{2}{3} \]
Calculating this gives:
\[ \text{Number of Green Marbles} = 24 \times \frac{2}{3} = 16 \]

### Step 4: Find the number of blue marbles
Now that we know there are 16 green marbles, we can find the number of blue marbles by subtracting the number of green marbles from the total number of marbles:
\[ \text{Number of Blue Marbles} = \text{Total Marbles} - \text{Number of Green Marbles} \]
Substituting the values we have:
\[ \text{Number of Blue Marbles} = 24 - 16 = 8 \]

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

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