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$\big(\frac{9}{10}\big)^5$
B$\frac{9}{10}$
C$10^{-5}$
D$\big(\frac{1}{2}\big)^2$
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A$\big(\frac{9}{10}\big)^5$
Let X denote the number of defective bulbs.
Hence, the binomial distribution is given by
$\text{n}=5,\text{p}=\frac{10}{100}=\frac{1}{10}$
$\& \text{ q}=\frac{90}{100}=\frac{9}{10}$
Hence, the distribution is given by
$\text{P(X = r})=\text{ }^5\text{C}_{\text{r}}\big(\frac{1}{10}\big)^{\text{r}}\big(\frac{9}{10}\big)^{5-\text{r}}$
$\therefore\text{P(X}=0)=\big(\frac{9}{10}\big)^5$
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