Question

In a box, consisting 100 bulbs, 10 are defective. The probability that out of a sample of 5 bulbs, none is defective is :

• A. 10^-1
• B. \((\frac{1}{2})^5\)
• C. \((\frac{9}{10})^5\)
• D. \((\frac{9}{10})\)

Answer 1

The Correct Option is C

To solve the problem of finding the probability that none of the bulbs in the sample are defective, let's follow these steps:

1. Total bulbs in the box = 100.

2. Number of defective bulbs = 10.

3. Number of non-defective bulbs = 100 - 10 = 90.

4. Probability of selecting a non-defective bulb = \(\frac{90}{100} = \frac{9}{10}\).

5. Since we need to find the probability that all 5 bulbs chosen are non-defective, and the events are independent, we multiply the individual probabilities:

\(P(\text{all 5 bulbs are non-defective}) = \left(\frac{9}{10}\right)^5\).

The correct answer is: \((\frac{9}{10})^5\).