What “condition” are you in? Launch
There are 54 students in the sophomore class. The Venn diagram below shows how many of
them take Geometry; play soccer, or do both.
______________
18
12
8
Take Geometry
Play Soccer
1. How many students are taking Geometry?
2. How many students play soccer?
3. How many students do both?
4. How many students do not play soccer and do not take Geometry?
5. How many students play soccer but do not take Geometry?
Use the data above to complete the frequency table below.
Takes Geometry
Plays Soccer
Does Not Play
Soccer
Total
Does Not Take
Geometry
Total
What “condition” are you in?
Name: ______________________
1. There are 150 children at summer camp and 71 signed up for swimming. There were a total
of 62 children that signed up for crafts and 28 of them also signed up for swimming.
Use the data above to complete the frequency table.
Takes Swimming
Classes
Does Not Take
Swimming Classes
Total
Makes Crafts
Does Not Make
Crafts
Total
a. How many campers did not take swim class or make crafts?
b. What percentage of the campers who did not take swimming lessons or make crafts?
c. Are campers more likely to take swimming lessons or make crafts? Explain your
reasoning.
d. Create a Venn diagram from this two-way table.
2. The table below represents data collected from a freshman survey of how 9th graders get to
school most often. Complete the two-way table:
Male
Female
Total
Walk
Car
28
45
Bus
12
27
Bike
17
69
Total
129
92
a. Suppose:
A = student is female
B = she walks to school
What is the probability a student walks to school, given the student is female? Rewrite
the question using conditional probability notation and write the probability as a fraction.
b. Suppose:
A = student is female
B = she walks to school
What is the probability a student is female, given the student walks to school? Rewrite
the question using conditional probability notation and write the probability as a fraction.
c. Are the fractions you wrote for questions a. and b. the same?
d. Suppose:
A = student is male
B= he rides the bus
What is the probability a student rides the bus, given the student is male? Rewrite the
question using conditional probability notation and write the probability as a fraction.
e. Suppose:
A = student is male
B= he rides the bus
What is the probability a student is male, given the student rides the bus to school?
Rewrite the question using conditional probability notation and write the probability as a
fraction.
f. Are the fractions you wrote for questions a. and b. the same?
g. From the above examples, you may conclude that the probabilities of event “A” given
condition “B” and event “B” given condition “A” are not the same, P(A|B) ≠ P(B|A). Explain
why this is the case and how you choose the numerator and denominator in this general case.
3. Heather, a hairdresser, is making a record of all the customers she had in the last month.
a. Provide row and column headings for the table below so it can show the number of male
and female customers who are adults and children.
Total
Total
b. In the last month she had 40 female children and only 5 male children.
Put these values in the table.
c. How many total children were customers last month?
d. She has 100 total customers and a total of 20 male customers during the same month.
Use this information to finish filling in your table.
e. Which of the cells represent a marginal probability?
f. Which of the cells represent a joint probability?
4. A large group of people was surveyed about their favorite movie genre. The participants
gave their age and chose their favorite movie genre, or type of movie, from Action, Comedy,
and Horror.
Action
Comedy
Horror
Total
18 - 25 years old
238
450
312
1,000
26 - 49 years old
350
472
178
1,000
50+ years old
320
490
190
1,000
Total
908
1,412
680
3,000
a. Find P(comedy | 26 - 49).
b. Find P(50+ | Horror)
c. Find P(Horror | 50+)
d. A company that sells a product designed for young adults wants to advertise at a movie.
Which genre should they choose? Explain your reasoning.
e. If the company wants to advertise to older adults, which genre would be least beneficial to
advertise in? Explain your reasoning.
5. Using the information in the launch question, write 3 conditional probability statements that
will have a large impact on the master schedule, for the guidance counselor to consider as the
master schedule is built.
What “condition” are you in?
Assessment
Name______________________
The two-way table below shows the number of houses of various styles in a large town.
Exterior
material
Brick
House
Color
Brown
Stucco
Aluminum
Siding
Wood
shakes
12
3
1
2
9
21
1
1
9
2
7
Blue
2
White
2
5
Red
1
3
Total
12
28
Total
1) What is P(brown house| aluminum siding), in fraction form?
2) What is P(aluminum siding| brown house), in fraction form?
3) Are your answers to 1) and 2) the same? Using the information in the table and your
fractions, explain your answer.
4) Explain your answer to 3) using another representation such as a picture, Venn diagram, or
tree diagram.
5) What is the probability that a house is brown? Is this joint or marginal probability?
6) What is the probability a house is red and made of stucco? Is this joint or marginal
probability?