Six jurors are to be selected from a pool of 20 potential candidates to hear a c

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 exactly 1.

Round your answer to four decimal places.

P(exactly 1) =

Explanation / Answer

Probability first juror selected is prejudiced is 3/20

Now assume the next five are not prejudiced then the calculation is

2/20 x 17/19 x 16/18 x 15/17 x 14/16 x 13/15 = 0.053216

Now repeat the calculation for the 2nd juror to be prejudiced, the third, the fourth etc.

so the final calculation is

6 x {2/20 x 17/19 x 16/18 x 15/17 x 14/16 x 13/15} = 0.319298

Thus,the probability that the number of potentially prejudiced jurors among the 6 selected jurors is exactly 1 is 0.3193 approximately.

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