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  • There are 5 % defective items in a large bulk of items. What is the probability that a sample of 10 items will include not more than one defective item?

Q. 3.     There are 5^{o}/_{o}  defective items in a large bulk of items. What is the probability that a sample of 10 items will include not more than one defective item?

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There are 5^{o}/_{o}  defective items in a large bulk of items.

X denotes the number of defective items in a sample of 10.

\Rightarrow \, \, P=\frac{5}{100}=\frac{1}{2}

\Rightarrow \, \, q=1-\frac{1}{20}=\frac{19}{20}

X has a binomial distribution, n=10.

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

           P(X=x)=^1^0C_x.(\frac{19}{20})^{10-x} . (\frac{1}{20})^{x}

P(not\, more\, than\, one\, defective item)=p(X\leq 1)

                                                                              =P(X=0)+P(X=1)

                                                                                  =^{10}C_0(\frac{19}{20})^{10} . (\frac{1}{20})^{0}+^{10}C_1(\frac{19}{20})^{9} . (\frac{1}{20})^{1} 

                                                                                  =(\frac{19}{20})^{9} . (\frac{29}{20})^{1}

Posted by

seema garhwal

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