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

(b) $\frac{9}{10}$

(c) 10⁻⁵

(d) ${\left(\frac{1}{2}\right)}^2$

Answer 1

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

Let X denote the number of defective bulbs.

Hence, the binomial distribution is given by

$$\begin{gathered} n=5,p=\frac{10}{100}=\frac{1}{10} \\ \&q=\frac{90}{100}=\frac{9}{10} \\ \mathrm{Hence},\mathrm{the}\mathrm{distribution}\mathrm{is}\mathrm{given}\mathrm{by} \\ P(\mathit{\text{X}}=r)={}^{5}C_{\mathit{r}}{\left(\frac{1}{10}\right)}^r{\left(\frac{9}{10}\right)}^{5-r} \\ \therefore P(X=0)={\left(\frac{9}{10}\right)}^5 \end{gathered}$$