It is know that a box of 600 electric bulbs contains 12 defective bulbs. One bulb is taken out at random from this box. What is the probability that it is a non-defective bulb?

Options

A. `578/600`
B. `49/50`
C. `1/50`
D. `12/600`

Answer

To solve the problem of finding the probability of selecting a non-defective bulb from a box of 600 electric bulbs containing 12 defective bulbs, we can follow these steps:

### Step-by-Step Solution:

**Step 1: Identify the total number of bulbs and defective bulbs.**
- Total number of bulbs = 600
- Number of defective bulbs = 12

**Step 2: Calculate the number of non-defective bulbs.**
- Number of non-defective bulbs = Total number of bulbs - Number of defective bulbs
- Number of non-defective bulbs = 600 - 12 = 588

**Step 3: Use the probability formula.**
- The formula for probability is given by:
\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]
- Here, the number of favorable outcomes (non-defective bulbs) = 588
- Total number of outcomes (total bulbs) = 600

**Step 4: Substitute the values into the probability formula.**
- Probability of selecting a non-defective bulb:
\[ \text{Probability} = \frac{588}{600} \]

**Step 5: Simplify the fraction.**
- To simplify \(\frac{588}{600}\), we can divide both the numerator and denominator by their greatest common divisor (GCD).
- The GCD of 588 and 600 is 12.
- Dividing both by 12:
\[ \frac{588 \div 12}{600 \div 12} = \frac{49}{50} \]

**Step 6: State the final answer.**
- The probability that a randomly selected bulb is non-defective is:
\[ \text{Probability} = \frac{49}{50} \]

### Final Answer:
The probability that the bulb taken out is non-defective is \(\frac{49}{50}\).

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