Conditional Probability

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 two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way 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

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