In a box containing 100 bulbs, 10 are defective. The probability that out of a sample of 5 bulbs none is defective, is :
- \(\frac{1}{10}\)
- \((\frac{1}{2})^5\)
- \((\frac{9}{10})^5\)
- \(\frac{9}{10}\)
The Correct Option is C
Solution and Explanation
To determine the probability that out of a sample of 5 bulbs none is defective, follow these steps:
1. Total Bulbs: There are 100 bulbs in total.
2. Defective Bulbs: There are 10 defective bulbs, thus there are \(100 - 10 = 90\) non-defective bulbs.
3. Sample Size: We are selecting a sample of 5 bulbs.
4. Probability of Selecting a Non-Defective Bulb: The probability of selecting a non-defective bulb on the first draw is \(\frac{90}{100} = \frac{9}{10}\).
5. Independent Events: Assuming that each selection is independent and that bulbs are replaced after each draw (or the probability remains the same approximately if they are not replaced due to a large total number), the probability that all 5 bulbs selected are non-defective is given by:
\[\left(\frac{9}{10}\right)^5\]
Therefore, the probability that none of the 5 bulbs selected is defective is \((\frac{9}{10})^5\).
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