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Suppose Nokia store places 20 of its cell phones on a clearance sale, unknown to anyone 5 of these cell phones are defective. A customer selects 3 cell phones at random for inspection. Let X be the number of defective cell phones in the sample. Find the probability distribution of X?

My attempt:

$$ \begin{matrix} x & 0 & 1 & 2 & 3 \\ P(X=x) & 0.015625 & 0.140625 & 0.421875 & 0.421875 \\ \\ \end{matrix} $$

I calculated the values using the binomial distribution: $$ P(X = x) = nCx \ p^{n-x} (1-p)^x$$

Where, $n$=5, $x$=0,1,2,3 and $p$=(.25) [from 5/20]

Is this the correct way to do this?

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    IF $p$ is the probability of detecting a faulty item ('success'), then it should be $\binom{n}{x}p^{x}(1-p)^{n-x}$2012-11-25
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    @Alex for sampling *with replacement*2012-11-25
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    Still, important to point out that even though Binomial is inappropriate, Binomial was mishandled.2012-11-25

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