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# A lot of 100 watches is known to have 10 defective watches.If 8 watches are selected(one by one with replacement) at random,what is the probability that there will be at least one defective watch?

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• $In\;a\;batch\;of\;100\;watches\;10\;are\;defective\;$
• $p(a\;watch\;selected\;is\;defective)=\large\frac{10}{100}=\frac{1}{10}$
• $p=\large\frac{1}{10}\;q=1-\frac{1}{10}=\frac{9}{10}$
• $8\;watches\;are\;selected\;n=8$
• $p=(X=r)\;=\;\Large\;c^n_r\;p^r\;q^{n-r}$
$p(at\;least\;1\;defective\;)=p(X\;\geq\;1)$
=$1-p(X\;<\;1)$
=$1-\;p(X\;=\;0)$
$=\Large\;1-c^8_o\;(\frac{1}{10})^0\;(\frac{9}{10})^8$
$=\Large\;1-(\frac{9}{10})^8$