Selecting an impartial jury can be a challenging endeavor. Take the case of George Zimmerman in the Trayvon Martin trial. Attourneys struggled to find a jury that was not biased against the defendant due exposure to media coverage. "I haven't lived under a rock for the past year, juror B-51, a white, female retiree, said" (Luscombe, 2013). Keeping the jury free of media coverage may ultimately mean sequestering the jury for the duration of the trial. Due to the widespread media coverage, all but four from a pool of hundreds of jury candidates were dismissed before reaching the formal questioning process. In the end, over 500 candidates were summoned in an effort to select a panel of six jurors and four alternates. Source: Luscombe, R. "Painfully slow progress in Zimmerman jury selection." The Guardian.com. 11 June 2013. Retrieved from http://www.theguardian.com/world/2013/jun/11/george-zimmerman-trayvon-martin-trial- If a jury pool consists of 10 men and 12 women, what is the probability of selecting a 5 person jury consisting of all females? Round your answer to the nearest whole number. Probability $=\square \%$ (Type an integer.)
Solution
Step 1 ：The total number of people in the jury pool is given by the sum of the number of men and women, which is \(10 + 12 = 22\).
Step 2 ：The total number of ways to select a 5 person jury from 22 people is given by the combination formula \(C(n, r) = \frac{n!}{r!(n-r)!}\), where \(n\) is the total number of items, \(r\) is the number of items to choose, and \(!\) denotes factorial. So, the total number of ways to select a 5 person jury from 22 people is \(C(22, 5) = \frac{22!}{5!(22-5)!} = 26,334\).
Step 3 ：The number of ways to select a 5 person jury consisting of all females from 12 women is \(C(12, 5) = \frac{12!}{5!(12-5)!} = 792\).
Step 4 ：The probability of selecting a 5 person jury consisting of all females is therefore \(\frac{792}{26,334} = 0.03008\).
Step 5 ：Rounding to the nearest whole number, the probability is 3%. So, the probability of selecting a 5 person jury consisting of all females is \(\boxed{3\%}\).
