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It is known that $10 \%$ of certain articles manufactured are defective. What is the probability that in a random sample of 12 such articles 9 are defective?
Solution:
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Verified Answer
$p=\frac{10}{100}=\frac{1}{10}, \mathrm{q}=1-\mathrm{p}=1-\frac{1}{10}=\frac{9}{10}$
$$
\begin{aligned}
&\mathrm{n}=12, \mathrm{r}=9, \mathrm{P}(\mathrm{X}=\mathrm{r})={ }^n C_r p^r q^{n-r} \\
&\mathrm{P}(\mathrm{X}=9)={ }^{12} C_9\left(\frac{1}{10}\right)^9\left(\frac{9}{10}\right)^3=\frac{220 \times 729}{(10)^{12}}
\end{aligned}
$$
In each of the following choose the correct answer.
$$
\begin{aligned}
&\mathrm{n}=12, \mathrm{r}=9, \mathrm{P}(\mathrm{X}=\mathrm{r})={ }^n C_r p^r q^{n-r} \\
&\mathrm{P}(\mathrm{X}=9)={ }^{12} C_9\left(\frac{1}{10}\right)^9\left(\frac{9}{10}\right)^3=\frac{220 \times 729}{(10)^{12}}
\end{aligned}
$$
In each of the following choose the correct answer.
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