#452 In a ground water contamination study

In a ground water contamination study - Math

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Free Chegg Question

In a ground water contamination study, the researchers identify 25 possible sites for drilling and sample collection. Unknown to the researchers, 19 of these sites have ground water with a high contamination, while the other 6 sites have ground water with a low contamination. The researchers have a budget that only allows them to drill at 5 sites, so they randomly choose these 5 sites from their list of 25 sites. What is the probability that at least 4 out of the 5 sites that the researchers examine have ground water with a high contamination?

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Free Chegg Answer

1. Step 1 of 3

   It was not known to the researchers that 19 out of 25 sites have ground water with high contamination and the rest have low contamination.

   The researchers randomly choose 5 sites as they are allowed to do so.

   Letdenotes the sites having high contamination anddenotes the sites having low contamination.

   So, the required distribution is the hypergeometric distribution with

   

   

   Let us consider,

   

   

   

   

2. Step 2 of 3

   From multivariate hypergeometric distribution, the probability mass function is given by,

   

3. Step 3 of 3

   Then, find the probability that at least 4 out of the 5 sites have ground water with high contamination.

   Now, from the given parameters we have

   

   

   OR, the probability that at least 4 out of the 5 sites have ground water with high contamination is.