Statistics and Probability Lesson Plan:
What is the Probability of the All-Female Zimmerman Jury?
Adapted from the Activity “How Fair is That Jury” in Navigating through Probability in Grades 9-12, National Council of
Teachers of Mathematics (NCTM)
Rewritten by Gary Abramsohn
Overview of Lesson
Working in pairs and with class discussion, students will analyze theoretical outcomes of gender in jury selections
and compare them with observed relative frequencies using random number generation to simulate empaneling a
jury. This will be an introduction to the binomial theorem and Pascal’s Triangle.
Common Core State Standards Grade Level Content
1. CCSS.Math.Content.HSS-CP.B.9 (+) Use permutations and combinations to compute probabilities of
compound events and solve problems.
2. CCSS.Math.Content.HSS-MD.A.3 (+) Develop a probability distribution for a random variable defined for a
sample space in which theoretical probabilities can be calculated; find the expected value. For example, find the
theoretical probability distribution for the number of correct answers obtained by guessing on all five questions
of a multiple-choice test where each question has four choices, and find the expected grade under various grading
schemes.
Common Core State Standards for Mathematical Practice
1. Make sense of problems and persevere in solving them.
2. Model with mathematics.
3. Use appropriate tools strategically.
Prerequisites
Students should know the addition rule and the multiplication rule for probability.
Students should know how to multiply binomials and polynomials.
A review session may be needed for both of the above prerequisites if students need more practice.
The math needed for this assignment should be able to be understood by ELLs, but if needed, there may need to
be interpretation for the meaning of “jury” and “juror” and “coin flip”.
Learning Objective
After an exploration activity and a class discussion including an explanation of the binomial theorem and Pascal’s
Triangle, students will connect the binomial theorem to the multiplication rule for probability. The students will
be able to apply binomial probability for two events with probabilities, p and q, where 𝑝 + 𝑞 = 1 and 𝑋 =
0,1,2,3 … 𝑛 for the number r “successes” in n trials using the probability distribution 𝑃(𝑋 = 𝑟) =
𝑛!
𝐶(𝑛, 𝑟)𝑝𝑟 𝑞 (𝑛−𝑟) where “n choose r” = 𝐶(𝑛, 𝑟) = (𝑛−𝑟)!𝑟! and 0 ≤ 𝑟 ≤ 𝑛. The students will recognize Pascal’s
Triangle in relation to the binomial theorem.
Time Required
This lesson will take place in one 75-minute lesson.
Materials Required
1/6
This lesson plan was developed during an Iowa Department of Education funded Mathematics and Partnership grant in 2013-2014 titled, "Statistics and
Probability for Teaching Secondary Students"



Each student will need a “What is the Probability of the Zimmerman Jury” activity page (attached).
Random number simulator (random number table or graphing calculator) for each pair of students. For coin
flips, the teacher can provide 6 coins (pennies) for each pair of students.
Binomial distribution simulation software demonstration for class.
Use this link to the Rossman/Chance Applet, Binomial Distribution at
http://www.rossmanchance.com/applets/BinomDist3/BinomDist.html . Enter the following:
“Probability of Success (π)” = 0.5, “Sample Size (n)” = 6, and “Number of Samples” = 40. Set the “Number
of Successes” ≥ 5. Click the “Draw Samples” radio button.
Instructional Lesson Plan
I.
Essential Questions or Big Mathematical Ideas
How likely is it that 5 or 6 women would be empaneled on a jury of 6 jurors.
What is a binomial distribution and how is it related to Pascal’s triangle?
II.
Launch
The lesson will start with a discussion of the empanelling of a jury for the July 2013 trial of George
Zimmerman with 6 women jurors empaneled. What is the likelihood of selecting 6 women, or 5 women
and 1 man for a 6 person jury? As the attorney for either the defendant or the state, would you find this to
be good or not so good for your case?
III.
Plan
 Discussion: Do the students remember the Zimmerman trial, and the fact that there were 6 female jurors?
 Pair students (using random method or by assignments, depending on class)
 Hand-out activity pages for each student.
 Read and discuss the opening paragraphs of the Activity Sheet.
 Have students work through questions 1 through 3 on the activity page, then have students volunteer to
present their work to their classmates.
 After a discussion of questions 1-3, have each student use a random number generator or coin flips to
simulate picking 40 different juries (question 4a).
 The students can pool their data for the 40 juries to produce a table of frequencies for all of their work.
 The students can use this pooled data to answer questions 4b and 4c.
 Use the Rossman Chance applet to show distributions of the jury makeup.
 Do the activity “Investigating Powers of Binomials”.
 Discuss the Binomial Theorem.
 Discuss Pascal’s Triangle.
 Use the binomial theorem to calculate the probability of a jury with 5 or 6 women out of 6 jurors.
 Use any extra time for questions about the lesson.
IV.
Close
By comparing the students’ empirical data to the theoretical result, the students will be able to relate the
two. If time permits, go over another example using the binomial theorem.
Assessment
The activity page for each student will be collected and assessed. A formative quiz will be given.
This lesson plan was developed during an Iowa Department of Education funded Mathematics and Partnership grant in 2013-2014 titled, "Statistics
and Probability for Teaching Secondary Students"
2/6
Formative Quiz Questions:
1. Given a coin that flips heads or tails with probabilities ℎ = .55 and 𝑡 = .45, find the probability that in five
consecutive flips, heads might come up four or five times in a row.
2. Given a jury pool that is 63% male and 37% female, find the probability of a 12-member jury that has 11 or 12
men empaneled.
Possible Extensions
Possible extensions would be using the understanding of a random variable and a binomial distribution to explore
the probabilities of other male/female combinations on a 12 person jury.
This lesson plan was developed during an Iowa Department of Education funded Mathematics and Partnership grant in 2013-2014 titled, "Statistics
and Probability for Teaching Secondary Students"
3/6
Name
Date
What is the Probability of the All-Female Zimmerman Jury?
Trayvon Martin was fatally shot by George Zimmerman on the night of February 26, 2012, in Sanford, Florida. Trayvon
Martin was a 17-year-old African American high school student. George Zimmerman, a 28-year-old mixed-race
Hispanic, was the neighborhood watch coordinator for the gated community where Martin was temporarily staying and
where the shooting took place. Following an earlier call from Zimmerman, police arrived within two minutes of a
gunshot during an altercation in which Zimmerman fatally shot Martin. Zimmerman was taken into custody, treated for
head injuries, and then questioned for five hours. The police chief said that Zimmerman was released for lack of evidence
and lack of legal grounds for arrest, and that Zimmerman had a right to defend himself with lethal force. However, six
weeks later, Zimmerman was charged with murder.
A jury of six women was empaneled, not by chance, but by design. According to an article in USA Today, Robert
Hirschhorn, a jury consultant with more than 28 years experience, told USA TODAY that women are better listeners, less
judgmental, and would more easily understand the fear Zimmerman felt when he shot Trayvon Martin. "I wanted to make
sure we were going to get jurors that would follow what the court of law required not what the court of public opinion
wanted," Hirschhorn said. "My number one goal was to get fair jurors that would really be able to listen to the evidence
and decide the case on facts and law not emotion."
For our assignment today, assume that in the pool of prospective jurors, the ratio of men to women is one to one and
remains constant throughout the jury selection process. Also assume that the defense team was able to empanel women
with a 70% probability. Let p be the probability of picking a female juror and q be the probability of picking a male juror.
Each selection is independent of every other one. Prospective jurors are selected until a 6-member jury panel is complete.
1a. What is the sample space for the 6 jurors who are men or women?
1a.
1b. List those outcomes that have 5 or more women.
2a. Use the multiplication rule to compute the probability of 5 women on the jury.
(𝑝 + 𝑞) = 1, so = 0.7 𝑎𝑛𝑑 𝑞 = 0.3 and there are 6 ways 5 women could be picked.
2a.
2b. Using the multiplication rule, calculate the probability of the outcome where there are six women on the jury.
2b.
2c. Calculate the probability of both outcomes for five or more women on the jury (use your answers for 2a and 2b and
the addition rule for probability).
2c.
3. If you were an attorney for the State in a case in which 5 or 6 women were initially called to
the jury, would you raise a question?
. Why or why not?
This lesson plan was developed during an Iowa Department of Education funded Mathematics and Partnership grant in 2013-2014 titled, "Statistics
and Probability for Teaching Secondary Students"
4/6
4a. Using a method to simulate randomly picking women or men for the jury, with a 70% chance of picking a female,
pick 40 separate juries. One way would be to place 7 of one color of M&Ms (representing females) and 3 of another color
of M&Ms (representing males) in a bag. Pick 6 M&Ms out of the bag and record the number of females picked for each
jury. Put the M&Ms back in the bag to pick again.
Record the number of women in each of your 40 simulated juries.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
21
22
23
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
4b. On the basis of your data, what is the probability of obtaining a jury on which there are at
least 5 women?
4c. How does your result in 4b compare with the probability for a jury of at least 5 women that
you calculated in question 2?
If the gender of one juror is independent from the gender of all prior jurors, and the probability p of picking a female juror
is 0.7, then the probability of picking a male juror 𝑞 𝑖𝑠 1 − 𝑝 = 0.3.
5a. Calculate the probability for 6 jurors with 5 females using Binomial Probability (𝑛𝑟)𝑝𝑟 𝑞 𝑛−𝑟 .
5b. Now calculate the probability for 6 jurors with 6 females using Binomial Probability.
5c. Add the answers for 5a and 5b.
5c.
5d. Compare your answer to 5c with your answer for 2c.
This lesson plan was developed during an Iowa Department of Education funded Mathematics and Partnership grant in 2013-2014 titled, "Statistics
and Probability for Teaching Secondary Students"
5/6
Exit Quiz – Zimmerman Jury
Name
Use Binomial Probability to solve:
Date
1. Given a coin that flips heads or tails with probabilities ℎ = .55 and 𝑡 = .45, find the probability that in five
consecutive flips, three will be heads.
2. Given a jury pool that is 63% male and 37% female, find the probability of a 12-member jury that has 11 or 12 men
empaneled.
This lesson plan was developed during an Iowa Department of Education funded Mathematics and Partnership grant in 2013-2014 titled, "Statistics
and Probability for Teaching Secondary Students"
6/6