A lot consists of 12 good pencils , 6 with minor defects and 2 with major defects .A pencil is chosen at random .Find the probability that this pencil is not defective.

Answer

To solve the problem step by step, we will determine the probability that a randomly chosen pencil from the lot is not defective.

### Step 1: Identify the total number of pencils
We are given:
- Good pencils = 12
- Pencils with minor defects = 6
- Pencils with major defects = 2

**Total number of pencils = Good pencils + Minor defect pencils + Major defect pencils**
\[ \text{Total pencils} = 12 + 6 + 2 = 20 \]

### Step 2: Identify the number of favorable outcomes
A pencil is considered not defective if it is a good pencil. Therefore, the number of favorable outcomes (good pencils) is:
\[ \text{Favorable outcomes} = 12 \]

### Step 3: Calculate the probability
The probability \( P \) of an event is given by the formula:
\[ P(\text{not defective}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]

Substituting the values we found:
\[ P(\text{not defective}) = \frac{12}{20} \]

### Step 4: Simplify the probability
To simplify \( \frac{12}{20} \):
\[ \frac{12}{20} = \frac{3}{5} \]

### Final Answer
The probability that the pencil chosen is not defective is:
\[ \frac{3}{5} \]

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