# Ch 5: Common Core HS Statistics & Probability: Probability

Share our high school statistics and probability video lessons with your students. Help them prepare to meet the common core standards for working with probability topics.

Standard: 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'). (CCSS.Math.Content.HSS-CP.A.1)

Standard: 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. (CCSS.Math.Content.HSS-CP.A.2)

Standard: 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. (CCSS.Math.Content.HSS-CP.A.3)

Standard: 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. (CCSS.Math.Content.HSS-CP.A.4)

Standard: 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. (CCSS.Math.Content.HSS-CP.A.5)

Standard: 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. (CCSS.Math.Content.HSS-CP.B.6)

Standard: 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. (CCSS.Math.Content.HSS-CP.B.7)

Standard: Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the model. (CCSS.Math.Content.HSS-CP.B.8)

Standard: Use permutations and combinations to compute probabilities of compound events and solve problems. (CCSS.Math.Content.HSS-CP.B.9)

A clear understanding of probability enables students to calculate the likelihood of simple, compound, complementary, independent and dependent events. They can use two-way tables to determine whether events are independent and to estimate conditional probabilities for real-life situations.

Our lessons for these standards address concepts such as:

• Elements, intersections and unions in mathematical sets
• Subsets of a sample space
• Probability of simple, compound, complementary, independent and dependent events
• Conditional probabilities
• Addition and multiplication rules and probability
• Probability of permutations

Students who grasp these concepts are able to calculate conditional probabilities, permutations and the probability of permutations. They can prepare for college and careers, where the ability to apply probability to research and real life situations is an asset.

### How to Use These Lessons in Your Classroom

The following are some tips for injecting lessons on probability into your curriculum to meet the common core standards:

#### Set the Purpose for Learning Lessons

Prior to viewing the videos, challenge your students to complete the corresponding quizzes for several of the following lessons: Mathematical Sets: Elements, Intersections & Unions; Probability of Simple, Compound and Complementary Events; Probability of Independent and Dependent Events; Probability of Independent Events: The 'At Least One' Rule; How to Calculate Simple Conditional Probabilities; How to Calculate a Permutation or How to Calculate the Probability of Permutations. Ask students to re-take the quizzes after completing the video lessons to assess understanding.

Watch the video lesson pertaining to probability and the addition rule. Using an online, interactive whiteboard or hand-held dies, multi-colored spinners and beads in jars, students will predict the possibilities. They will then roll/spin/choose, using technology or manipulatives, and note the outcomes. Discuss and discover how the addition rule applies to their results.

#### Conditional Probabilities, Independent Events and Multiplication Rule Lessons

Share the pertinent videos from the topics listed above. Using a standard deck of cards, determine the probability that the first card chosen will be a named face card and the second card picked will be another specified face card without the first one being replaced in the deck. Discuss why the events are dependent and why the probability has changed. Guide the students in using the multiplication rule to calculate the probability of events.

14 Lessons in Chapter 5: Common Core HS Statistics & Probability: Probability
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Chapter Practice Exam
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Practice Final Exam
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