A box contains 100 bulbs out of which 10 are defective. A sample of 5 bulbs is drawn. The probability that none is defective , is

Options

A. `10^(-5)`
B. `2^(-5)`
C. `(0.9)^5`
D. `0.9`

Answer

To solve the problem step by step, we need to calculate the probability that none of the 5 bulbs drawn from a box of 100 bulbs (10 of which are defective) are defective.

### Step-by-Step Solution:

1. **Identify the Total and Defective Bulbs:**
- Total bulbs = 100
- Defective bulbs = 10
- Non-defective bulbs = Total bulbs - Defective bulbs = 100 - 10 = 90

2. **Determine the Probability of Selecting a Non-defective Bulb:**
- The probability of selecting a non-defective bulb (success) is:
\[ P(\text{non-defective}) = \frac{\text{Number of non-defective bulbs}}{\text{Total number of bulbs}} = \frac{90}{100} = 0.9 \]

3. **Calculate the Probability of Selecting 5 Non-defective Bulbs:**
- Since we are drawing 5 bulbs, and we want all of them to be non-defective, we can use the formula for the probability of independent events:
\[ P(\text{none defective}) = P(\text{non-defective})^5 = (0.9)^5 \]

4. **Compute \( (0.9)^5 \):**
- Calculate \( 0.9^5 \):
\[ 0.9^5 = 0.59049 \]

5. **Final Answer:**
- The probability that none of the 5 bulbs drawn is defective is approximately:
\[ P(\text{none defective}) \approx 0.59049 \]