In a box containing 100 bulbs, 10 are defective. The probability that out of a sample of 5 bulbs, none is defective is A. 10^{-1}
B. (1 / 2)^{5}
C. (9 / 10)^{5}
D. 9 / 10
In a box containing 100 bulbs, 10 are defective. The probability that out of a sample of 5 bulbs, none is defective is A. 10^{-1}
B. (1 / 2)^{5}
C. (9 / 10)^{5}
D. 9 / 10

Solution:
Answer: C. (9 / 10)^{5}

Explanation:

Assume X is the number of times a random sample of 5 bulbs was selected for faulty bulbs.

Bernoulli trials are also the process of repeatedly selecting damaged bulbs from a package. We have, obviously, {X} has the binomial distribution where \mathrm{n}=5 and \mathrm{p}=1 / 10

And, q=1-p=1-1 / 10

\therefore P(X=x)={ }^{n} C_{x} q^{n-x} p^{x}
={ }^{5} C_{x}\left(\frac{9}{10}\right)^{5-x}\left(\frac{1}{10}\right)^{x}

Hence, probability that none bulb is defective =\mathrm{P}(\mathrm{X}=0)
={ }^{5} C_{0} \cdot\left(\frac{9}{10}\right)^{5}

=1 \cdot\left(\frac{9}{10}\right)^{5}
=\left(\frac{9}{10}\right)^{5}

\therefore Option \mathrm{C} is correct