UNIT 3:

Probability

(4 weeks)

GHS Department of Matheππππatics

I n t e g r a t e d M a t h 3 – U n i t 3 – P r o b a b i l i t y Page 2

Int. Math 3: Probability (4 weeks)

I Can . . . Vocabulary • I can define event and sample space. • I can establish events as subsets of a sample space. • I can define union, intersection, and complement. • I can establish events as subsets of a sample space based on the union, intersection, and/or

complement of other events. • I can define and identify independent events and justify my conclusions. • I can explain and provide an example to illustrate that for two independent events, the probability of the

events occurring together is the product of the probability of each event. • I can calculate the probability of an event. • I can predict if two events are independent, explain my reasoning, and check my statement by

calculating P(A and B) and P(A) x P(B). • I can define dependent events and conditional probability. • I can explain that conditional probability is the probability of an event occurring given the occurrence of

some other event and give examples that illustrate conditional probability. • I can explain that for two events A and B, the probability of event A occurring given the occurrence of

event B is � ���� � �� �� �

�� and give examples to show how to use the formula.

• I can explain that A and B are independent events if the occurrence of A does not impact the probability of B occurring and vice versa.

• I can determine when a two-way frequency table is an appropriate display for a set of data. • I can collect data from a random sample. • I can construct a two way frequency table. • I can pose a question for which a two-way frequency is appropriate, use statistical techniques to sample

the population, and design an appropriate product to summarize the process and report the results. • I can illustrate the concept of conditional probability and independence using everyday examples of

dependent and independent events respectively. • I can apply the fundamental counting principle to find the total number of possible outcomes in a sample

space. • I can define factorial, permutation, combination, and compound event. • I can distinguish between situations that require permutations and those that require combinations. • I can apply the permutation formula and the combination formula. • I can compute probabilities of an event. • I can write and solve original problems involving compound events, permutations, and/or combinations. • I can use probability to create a method for making a fair decision. • I can use probability to analyze the results of a process and decide if it resulted in a fair decision. • I can analyze data to determine whether or not the best decision was made. • I can define population and population parameter. • I can explain why randomization is used to draw a sample that represents a population well. • I can recognize that statistics involves drawing conclusions about a population based on the results

obtained from a random sample of the population. • I can choose a probability model for a problem situation. • I can conduct a simulation of the model and determine which results are typical of the model.

• Event • Sample space • outcome • Subset • Union • Intersection • Complement • Independent events • Dependent events • Probability • Product event • Conditional probability • Two-way frequency

table • Display • Data • random sample • fundamental counting

principle. • Factorial • Permutation • Combination • Simulation • Fair • Theoretical probability • Experimental

probability • model

Common Core State Standards • 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”) • 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 their probabilities, and use this characterization to determine if they are independent. • 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 A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B

• 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.

• S.CP.5 Recognize and explain 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.

• S.CP.9 (+) Use permutations and combinations to compute probabilities of compound events and solve problems • S.MD.6 (+) Use probability to evaluate outcomes of decisions. Use probabilities to make fair decisions (e.g., drawing

by lots, using a random number generator). • S.MD.7 (+) Use probability to evaluate outcomes of decisions. Analyze decisions and strategies using probability

I n t e g r a t e d M a t h 3 – U n i t 3 – P r o b a b i l i t y Page 3

concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game) • S.IC.1 Understand statistics as a process for making inferences about population parameters based on a random

sample from that population • S.IC.2 Decide if a specified model is consistent with results from a given data-generating process, e.g., using

simulation. For example, a model says a spinning coin falls head side up with probability 0. 5. Would a result of 5 tails in a row cause you to question the model?

Standards for Mathematics Practices � Make sense of problems and persevere in solving problems. � Reason abstractly and quantitatively. � Construct viable arguments and critique the reasoning of

others. � Model with mathematics.

� Use appropriate tools strategically. � Attend to precision. � Look for and make use of structure. � Look for and express regularity in repeated reasoning.