#### Question

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

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

\[\frac{9}{10}\]

10

^{−5}\[\left( \frac{1}{2} \right)^2\]

#### Solution

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

Let *X* denote the number of defective bulbs.

Hence, the binomial distribution is given by

\[n = 5 , p = \frac{10}{100} = \frac{1}{10}\]

& \[ q = \frac{90}{100} = \frac{9}{10}\]

\[\text{ Hence, the distribution is given by } \]

\[P(X = r) = ^{5}{}{C}_r \left( \frac{1}{10} \right)^r \left( \frac{9}{10} \right)^{5 - r} \]

\[ \therefore P(X = 0) = \left( \frac{9}{10} \right)^5\]

Is there an error in this question or solution?

Solution In a Box Containing 100 Bulbs, 10 Are Defective. What is the Probability that Out of a Sample of 5 Bulbs, None is Defective? Concept: Bernoulli Trials and Binomial Distribution.