INa box containing 100 bulbs, 10 are defective. What is the probability that out of a sample of 5 bulbs none is defective?

$\left(\frac{9}{10}\right)^5$

We have,

p= Probability that a bulb is defective $= \frac{10}{100}=\frac{1}{10}$

$∴ q= 1 -p =\frac{9}{10}$

Let X be the number of defective bulbs in a sample of 5 bulbs.

Then, X follows binomial distribution with n = 5, $p=\frac{1}{10}$ and $q= \frac{9}{10}$ such that

$P(X =r)= {^5C}_r\left(\frac{1}{10}\right)^r\left(\frac{9}{10}\right)^{5-r}, r= 0, 1, ...,5$

∴ Required probability $= P(X=0)$

$= {^5C}_0\left(\frac{1}{10}\right)^0\left(\frac{9}{10}\right)^{5}=\left(\frac{9}{10}\right)^{5}$