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HCPSS Worthwhile Math Task
Common Characteristics
Common Core Standard
S.CP.B.6 Find the conditional probability of A given B as the fraction of B’s outcomes that also
belong to A ,and interpret the answer in terms of the model.
MP2:
MP3:
MP4:
MP7:
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Look for and make use of structure.
Common Core Geometry, Unit 5
The Task
In your group, find three characteristics or interests that two or more members of the group have
in common. Label them A, B, and C.
List your sample space and create a way of displaying the sample space showing the three
characteristics. It could be color coding, circling, starring, highlighting, etc.
1. List the probabilities of selecting a student with each characteristic.
2. Find the probability that a student has both characteristics A and B.
3. Given that the person selected has characteristic B, what is the probability that they have
characteristic A?
4. How are the first two questions related to the third?
Each group will present their findings to the class. Bonus points for the most creative group!
Facilitator Notes
1. Have students form groups of 5 or 6.
2. Have students read the task. If needed, provide some sample characteristics, such as
“have brown hair,” “like the beach,” “have driver’s license,” etc.
3. Give students three minutes to determine characteristics, and then they need to begin
working on how to display the information. (Look for evidence of MP2.)
4. Have the groups present their solutions. As a class, discuss the similarities and difference
between groups. (Look for evidence of MP3.)
5. Present the following problem for students to discuss:
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has
licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0
Unported License.
HCPSS Worthwhile Math Task
“In a group of 50, 10 people are wearing glasses. Of the people wearing shorts, 10% wear
glasses. How many people are wearing shorts and glasses?” (Look for evidence of MP2
and MP3.)
Follow-Up Questions
1. How did your group organize your sample space to help find the probabilities? Look for
evidence of MP4, and MP7.)
2. What strategies did your group use to determine the probabilities?
3. Which question was most difficult and why?
Extension Questions:
1. In a previous election, 45 voters were registered Republican, 45 were registered
Democrats, and 10 were registered Independent. In the actual voting, 15 of the Democrats
voted for the Republican candidate. Given that the voter was registered Democrat, what
is the probability that the voter voted for the Republican candidate?
2. You school is trying to determine how many conflicts they will have for school pictures
this year. The yearbook team knows that ¼ of the students are freshman. Of the
freshman, 5% are in band. What percent of the students are freshman in band?
Solutions
Characteristics: Students wearing red (A), students wearing shorts (B), and students in the school
musical (C)
Sample Space: Molly, Joe, Juan, Tanisha, and Zach
A: Wearing Red: Molly, Zach, and Juan
B: Wearing shorts: Joe, Tanisha, and Zach
C: In the musical: Joe, Tanisha, and Juan
Red
Shorts
Zach
Molly
Juan
Joe
Tanisha
Musical
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has
licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0
Unported License.
HCPSS Worthwhile Math Task
1. P(Shorts) = 3/5
P(Red) = 3/5 P(Musical) = 3/5
2. P(Red and Shorts) = 1/5
3. P(Red|Shorts) = 1/3
1/ 5 1

4. P(Red|Shorts) =
3/5 3
Probability of A given B is equal to the probability of A and B divided by the probability of
B.
Follow-Up Question Sample Answers:
1. We listed each of the groups separately. Then we created a Venn diagram of the
characteristics. This way, we could easily see who had which characteristics out of the
entire group.
2. Our group sorted our members into smaller groups. For example, when we wanted to find
the probability that a member is wearing red given that they’re wearing shorts, we only
looked at the people who were wearing shorts and then counted how many students were
also wearing red.
3. The fourth problem was most difficult because we knew the probability from counting
but weren’t sure how to get the probability from the other two.
Answer Discussion Question:
One person is wearing shorts and glasses
Extension Question Answers:
1. 15/45 = 1/3
2. P(Band|Freshman) = 1/20
P(Freshman) = ¼
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has
licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0
Unported License.