Question

In a box containing 100 bulbs, 10 are defective. The probability that out of 20 bulbs selected at random, none is defective is

• A. \( 10 \left( \frac{1}{10} \right)^{20} \)
• B. \( 20 \left( \frac{9}{10} \right)^{20} \)
• C. \( 5 \left( \frac{1}{10} \right)^{20} \)
• D. \( \left( \frac{9}{10} \right)^{20} \)

Hint:

When calculating probabilities in a selection without replacement, use the individual probability for each selection and multiply them together.

Answer 1

The Correct Option is D

Step 1: Use the probability formula.
The probability of selecting a non-defective bulb is \( \frac{9}{10} \). Since we are selecting 20 bulbs, the probability that none of them is defective is: \[ P(\text{none defective}) = \left( \frac{9}{10} \right)^{20} \] Step 2: Conclusion.
The correct answer is (D) \( \left( \frac{9}{10} \right)^{20 \)}.