In a box containing 100 bulbs, 10 are defective. The probability that out of a sample of 5 bulbs none is defective, is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(\left(\displaystyle\frac{9}{10}\right)^5\)
Each bulb drawn is defective with probability
\( \displaystyle p = \frac{10}{100} = \frac{1}{10} \)
so it is good with probability
\( \displaystyle q = 1 - \frac{1}{10} = \frac{9}{10} \)
As usual in such questions, the 5 bulbs are treated as 5 independent trials with the same probability (Bernoulli trials). The number X of defective bulbs then follows the binomial distribution with n = 5, p = \(\frac{1}{10}\), and "none defective" means all 5 trials give a good bulb:
\( \displaystyle P(X = 0) = q^{5} = \left(\frac{9}{10}\right)^5 \)