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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?

Q. 13  It is known that  10^{o}/_{o}  of certain articles manufactured are defective. What is the probability that in a random sample of 12 such articles,9 are defective?

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best_answer

Let X represent a number of times selecting defective items out of 12 articles.

Probability of getting a defective item =P

        P=10\%=\frac{10}{100}=\frac{1}{10}

        q=1-P=1-\frac{1}{10}=\frac{9}{10}

X has a binomial distribution,n=12

\therefore \, \, \, \, P(X=x)=^nC_x.q^{n-x}.p^x

                P(X=x)=^1^2C_x.(\frac{9}{10})^{12-x} . (\frac{1}{10})^{x}

                    P(selectting\, \, 9\,defective \, items)=

                                                                               =^{12}C_9 (\frac{9}{10})^{3}\frac{1}{10}^9

                                                                              =220 (\frac{9^3}{10^3})\frac{1}{10^9}

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

Posted by

seema garhwal

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