(Solved) Six jurors are to be selected from a pool of 20 potential candidates to hear a civil case involving a lawsuit between two families. Unknown to the judge or any of the attorneys, 4 of the 20 prospective jurors are potentially prejudiced by being acquainted with one or more of the litigants. They will not disclose this during the jury selection process. If 6 jurors are selected at random from this group of 20, find the probability that the number of potentially prejudiced jurors among the 6 selected jurors is a. exactly 1 b. none c. at most 2

Question:

Six jurors are to be selected from a pool of 20 potential candidates to hear a civil case involving a lawsuit between two families. Unknown to the judge or any of the attorneys, 4 of the 20 prospective jurors are potentially prejudiced by being acquainted with one or more of the litigants. They will not disclose this during the jury selection process. If 6 jurors are selected at random from this group of 20, find the probability that the number of potentially prejudiced jurors among the 6 selected jurors is

a. exactly 1 

b. none 

c. at most 2

Explanation:

Detailed explanation is provided in below:

Part (a) explanation:

Here 6 jurors are selected at random from this group of 20. So total number of ways = 20C6 

Deniminator is 20C6. Further explanation is provided below. 

Part (b) explanation:

Part(c) explanation:

Final Answers:

(a) Probability that the number of potentially prejudiced jurors among the 6 selected jurors is exactly 1 = 0.4508

(b) Probability that the number of potentially prejudiced jurors among the 6 selected jurors is none = 0.2066

(c) Probability that the number of potentially prejudiced jurors among the 6 selected jurors is/are at most 2= 0.9391

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