A pencil box has 5 fountain pens. 3 blue pencils. And 7 red pencils. One item is taken out of the box at random. Find the probability that the item is a:
pencil

Answer

To find the probability that the item taken out of the pencil box is a pencil, we can follow these steps:

### Step 1: Identify the total number of items in the pencil box.
- The pencil box contains:
- 5 fountain pens
- 3 blue pencils
- 7 red pencils

**Calculation:**
Total items = Number of fountain pens + Number of blue pencils + Number of red pencils
Total items = 5 + 3 + 7 = 15

### Step 2: Identify the total number of favorable outcomes (pencils).
- The favorable outcomes are the total number of pencils, which includes both blue and red pencils.

**Calculation:**
Total pencils = Number of blue pencils + Number of red pencils
Total pencils = 3 + 7 = 10

### Step 3: Use the probability formula.
- The formula for probability is given by:

\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]

**Calculation:**
Probability of selecting a pencil = \(\frac{\text{Total pencils}}{\text{Total items}} = \frac{10}{15}\)

### Step 4: Simplify the probability.
- We can simplify \(\frac{10}{15}\) by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 5.

**Calculation:**
\[ \frac{10 \div 5}{15 \div 5} = \frac{2}{3} \]

### Final Answer:
The probability that the item taken out of the box is a pencil is \(\frac{2}{3}\).

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