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?