Question

Six jurors are to be selected from a pool of potential candidates to hear a civil case involving a lawsuit between two families. Unknown to the judge or any of the attorneys, of the 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 jurors are selected at random from this group of , find the probability that the number of potentially prejudiced jurors among the selected jurors is exactly .

Answer 1

The question involves calculating the probability of selecting six potentially prejudiced jurors for a civil case, which requires additional specific information not provided. Without the total number of biased and unbiased jurors, we cannot compute the probability. The importance of an impartial jury in legal proceedings is emphasized, aligning with the Sixth and Seventh Amendments.

Step-by-step explanation:

The subject of the question is Mathematics, specifically in the area of probability and combinatorics. The student is asked to find the probability of selecting exactly six potentially prejudiced jurors out of an unspecified number of candidates for a civil case.

To calculate this probability, we would usually use combinations to find the total number of ways to select six jurors from the total pool, and the number of ways to select six prejudiced jurors from those that are prejudiced. However, the question does not provide the total number of biased or unbiased jurors, which is necessary information for solving the problem. Therefore, we cannot calculate a specific probability here without additional information.

In a broader sense, the integrity of the jury selection process is crucial for ensuring the right to a fair trial, as entrenched in the Sixth and Seventh Amendments. An impartial jury is a cornerstone of the legal process, both in criminal and civil cases, and any biases in the jury can undermine the fairness and outcome of a trial.

Answer 2

Complete 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, 2 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

Answer:

0.442 ; 0.479 ; 1

Step-by-step explanation:

Given:.

Total number of candidates = 20

Number of jurors to be selected = 6

Number of prejudiced jurors = 2

Required outcome / Total possible outcomes :

Using the combination formula :

nCr = n! ÷ (n-r)!r!

1.)

P(number of prejudiced jurors is exactly 1) :

[2C1 * 18C5] ÷ 20C6

(2*8568)÷ 38760

= 0.442

B.)

P(None of the jurors is prejudiced) :

[2C0 * 18C6] ÷ 20C6

(1 * 18564) ÷ 38760

= 0.479

C.)

P(at most 2 of the jurors are prejudiced)

P(x =0) + p(x = 1) + p(x = 2)

P(x = 2) :

[2C2 * 18C4] ÷ 20C6

(1 * 3060) ÷ 38760

= 0.079

P(x =0) + p(x = 1) + p(x = 2)

(0.479 + 0.442 + 0.079)

= 1