Standard

Essential
Question

Bloom’s
Taxonomy Activities

Vocabulary

Pacing

S.CP.1 Describe events as subsets of a
sample space (the set of outcomes) using characteristics (or categories) of
the outcomes, or as unions, intersections, or complements of other events
(“or,” “and,” “not”).

Why are
subsets relevant to areas beyond mathematics?

Create
and solve a word problem which uses unions and intersections of sets.

Set
Subset
Union
Intersection
Sample
space
Outcomes

1 day

S.CP.2
Understand that two events A and B are independent if the probability
of A and B occurring together is the product of the probabilities, and use
this characterization to determine if they are independent

How can
one check if two events are independent of each other?

Compare
and contrast the probabilities of two events to determine if the events are
independent.

Independent
Probabilities

1 day

S.CP.3 Understand the conditional
probability of A given B as P(A and B)/P(B), and
interpret independence of A and B as saying that the conditional
probability of B given A is the same as the probability of B.

In what
areas are conditional probabilities relative to everyday life?

Create a
Venn Diagram and determine the probabilities of each occurrence.

Conditional
probability
Venn
diagram

1 day

S.CP.4 Construct and interpret twoway frequency
tables of data when two categories are associated with each object being
classified. Use the twoway table as a sample space to decide if events are
independent and to approximate conditional probabilities. For example, collect data from a random
sample of students in your school on their favorite subject among math,
science, and English. Estimate the probability that a randomly selected
student from your school will favor science given that the student is in
tenth grade. Do the same for other subjects and compare the results.

How are
frequency tables used to foresee possible election results?

From
Common Core:
Collect
data from a random sample of students in your school on their favorite
subject among math, science, and English. Estimate the probability that a
randomly selected student from your school will favor science given that the
student is in tenth grade. Do the same for other subjects and compare the
results.

Frequency
Table

1 day

S.CP.5 Recognize and explain in the concepts
of conditional probability and independence in everyday language and everyday
situations. For example, compare the
chance of having lung cancer if you are a smoker with the chance of being a
smoker if you have lung cancer.

How do
meteorologists utilize probability to forecast weather?

From
Common Core:
Compare the chance of having lung cancer
if you are a smoker with the chance of being a smoker if you have lung
cancer.

Conditional
probability
Independence
of events

1 day

S.CP.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.

How does
ratio relate to conditional probability?

Complete
the following problem from Dartmouth College and create a similar problem:
one finds that in a population of 100,000 females, 89.835% can expect to live
to age 60, while 57.062% can expect to live to age 80. Given that a woman is
60, what is the probability that she lives
to age
80?

Conditional
probability
Outcomes

1 day

S.CP.7
Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B), and interpret
the answer in terms of the model

What is
the connection between intersection, union, and the Addition Rule?

Using a
deck of cards, create a worksheet which requires the use of addition rule.
Share your worksheet with your peers.

Addition
rule
Probability
Venn
Diagram

1 day

S.CP.8 (+) Apply the general
Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(BǀA) =
P(B)P(AǀB), and interpret the answer in terms of the model.

How does
the multiplication rule relate to independent and dependent events?

Using a
bag of candy, create a worksheet utilizing the Multiplication Rule with seven
examples of picking candy in a particular order.

Multiplication
Rule

1 day

S.CP.9 (+) Use permutations and
combinations to compute probabilities of compound events and solve problems.

What is
the difference between a permutation and a combination?

Develop a
worksheet in which your peers must determine if the question requires a
permutation or a combination.
http://www.regentsprep.org/Regents/math/algtrig/ATS5/PCPrac.htm

Permutations
Combinations

1 day
