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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?

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?

Answers (1)

Solution

Given-

There are 10 defective watches in 100 watches

The probability of a defective watch from a lot of 100 watch =\frac{10}{100}=\frac{1}{10} 

P=\frac{1}{10},q=\frac{9}{10}, n=8$ and $r \geq 1
As we know that

\\\mathrm{P}(\mathrm{X})=^\mathrm{n}{\mathrm{c}_{\mathrm{r}}}(\mathrm{p})^{\mathrm{r}} \mathrm{q}^{\mathrm{n}-\mathrm{r}} \\\therefore \mathrm{P}=(\mathrm{r} \geq 1)=1-\mathrm{P}(\mathrm{r}=0) \\=1-^8{c_{0}}\left(\frac{1}{10}\right)^{0}\left(\frac{9}{10}\right)^{8-0} \\=1-\frac{8 !}{0 ! 8 !} \times\left(\frac{9}{10}\right)^{8} \\=1-\left(\frac{9}{10}\right)^{8}\\ = 0.56953279\approx 0.57

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infoexpert22

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