Out of 250 bulbs in a box, 35 bulbs are defective. One bulb is taken out at random from the box. Find the probability that the drawn bulb is not defective.

Answer

To find the probability that a randomly drawn bulb from a box of 250 bulbs is not defective, we can follow these steps:

### Step 1: Identify the total number of bulbs
The total number of bulbs in the box is given as 250.

### Step 2: Identify the number of defective bulbs
The number of defective bulbs is given as 35.

### Step 3: Calculate the number of non-defective bulbs
To find the number of non-defective bulbs, we subtract the number of defective bulbs from the total number of bulbs:
\[ \text{Number of non-defective bulbs} = \text{Total bulbs} - \text{Defective bulbs} = 250 - 35 = 215 \]

### Step 4: Use the probability formula
The probability \( P \) of an event is given by the formula:
\[ P(\text{not defective}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]
In this case, the number of favorable outcomes (non-defective bulbs) is 215, and the total number of outcomes (total bulbs) is 250.

### Step 5: Substitute the values into the formula
Substituting the values we found:
\[ P(\text{not defective}) = \frac{215}{250} \]

### Step 6: Simplify the fraction
To simplify \(\frac{215}{250}\), we can divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 215 and 250 is 5.
\[ \frac{215 \div 5}{250 \div 5} = \frac{43}{50} \]

### Final Answer
Thus, the probability that the drawn bulb is not defective is:
\[ \boxed{\frac{43}{50}} \]

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