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. `(1/2)^(5)`
B. `9/10`
C. `(9/10)^(5)`
D. `(1/10)^(5)`

Answer

To solve the problem of finding the probability that none of the 5 bulbs drawn from a box of 100 bulbs (where 10 are defective) is defective, we can follow these steps:

### Step-by-Step Solution:

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

2. **Calculate the Probability of Selecting a Non-Defective Bulb:**
- Probability of selecting a non-defective bulb = Number of non-defective bulbs / Total number of bulbs
- Probability (non-defective) = 90 / 100 = 0.9

3. **Determine the Probability of Selecting 5 Non-Defective Bulbs:**
- Since we want the probability that all 5 selected bulbs are non-defective, we can use the multiplication rule for independent events.
- Probability (all 5 non-defective) = (Probability of one non-defective bulb) ^ 5
- Probability (all 5 non-defective) = (0.9)^5

4. **Calculate (0.9)^5:**
- (0.9)^5 = 0.59049

5. **Final Result:**
- The probability that none of the 5 bulbs drawn is defective is approximately 0.59049.

### Conclusion:
The probability that none of the 5 bulbs drawn is defective is **0.59049**.

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