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?

Explanation

Probability of defective watch out of `100` watches`=frac{10}{100}=frac{1}{10}`

Here,` n=8`

`p=frac{1}{10} `

`q=1-frac{1}{10}=frac{9}{10}`

And` r geq 1`

`P(X geq 1)=1-P(x=0) `

`=1-^{8} C_{0}(frac{1}{10})^{0}(frac{9}{10})^{8-0} `

`=1-(frac{9}{10})^{8}`

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