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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?
CBSE | Class 12 | Maths | NCERT | Probability
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?

Solutions:

Assume that X is the number of times a defective article was selected from a random sample space of 12 articles.

Bernoulli trials are also repeated articles in a random sample space.

Obviously, we have \mathrm{X} has the binomial distribution where \mathrm{n}=12 and \mathrm{p}=10 \%=1 / 10 And, q=1-p=1-1 / 10=9 / 10

\therefore P(X=x)={ }^{n} C_{x} q^{n-x} p^{x}
={ }^{12} C_{x}\left(\frac{9}{10}\right)^{12^{-x}} \cdot\left(\frac{1}{10}\right)^{x}

Hence, probability of selecting 9 defective articles ={ }^{12} C_{9}\left(\frac{9}{10}\right)^{3}\left(\frac{1}{10}\right)^{9}

=220 \cdot \frac{9^{3}}{10^{3}} \cdot \frac{1}{10^{9}}
=\frac{22 \times 9^{3}}{10^{11}}

i

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