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Problem 96: Among the 12 solar collectors on display at a trade show, 9 are flat-platecollectors and the others are concentrating collectors. If a person visiting the show randomly selects 4 of te solar collectors to check out, what is the probability that 3 of them will be flat plate collectors?

Problem 96: Among the 12 solar collectors on display at a trade show, 9 are flat-platecollectors and the others are concentrating collectors. If a person visiting the show randomly selects 4 of te solar collectors to check out, what is the probability that 3 of them will be flat plate collectors?

Solution:


Given that $x=3,n=4,a=9, N=12$
Hypergeometric distribution, $h(x;n,a,N)=\frac{\left(\begin{array}{c}a\\ x\end{array}\right)\left(\begin{array}{c}N-a\\ n-x\end{array}\right)}{\left(\begin{array}{c}N\\ n\end{array}\right)}$
$h(3;4,9,12)=\frac{\left(\begin{array}{c}9\\ 3\end{array}\right)\left(\begin{array}{c}12-9\\ 4-3\end{array}\right)}{\left(\begin{array}{c}12\\ 4\end{array}\right)} = 0.5091.$

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