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PA-D-2-3

Page history last edited by Tashe Harris 6 years, 1 month ago

PA.D.2.3 Compare and contrast dependent and independent events.


In a Nutshell

After calculating simple probabilities, students will explore compound probabilities that are either independent or dependent events and are products of two probabilities. The events of two probabilities are said to be independent if the results of the second event is not affected by the result of the first event. In fact, the independent events can be calculated in reverse order before finding their product and will produce an equivalent outcome. The events of two probabilities are said to be dependent if the result of the second event is affected by the result of the first event. 

Student Actions

Teacher Actions

  • Develop a Deep and Flexible Conceptual Understanding by comparing and contrasting simple and compound probability questions, derive that compound probability asks similar questions to simple probability, but has more than 1 desired outcome or event.

  • Develop Ability to Make Conjectures, Model and Generalize when describe how words like “and” “or” “with replacement” and “without replacement” affect the probability of an event occurring. 

  • Develop Mathematical Reasoning when calculating compound probability, explore the ideas of dependence and independence by analyzing if and how the first desired event effects the sample space of the second desired event.

  • Implement tasks that promote reasoning and problem solving by giving students activities to calculate compound probability using words like “and” “or” “with replacement” and “without replacement”.

  • Facilitate meaningful mathematical discourse by emphasizing the idea of dependence in compound probabilities by having students explain what happens to the sample space after the first event occurs. If it remains the same, the events are independent. If it changes, the events are dependent. 

  • Pose purposeful questions when using  real life examples (like the lottery) for students to have a real life context of dependent compound probability.  Ask students to explain their reasoning and determine what makes events independent or dependent.

Key Understandings

Misconceptions

  • Calculate Compound probability with and without replacement.

  • An independent event occurs when the second event is not affected by the first event

  • A dependent event occurs when the  second event is affected by the first event

  • Identify independent and dependent events in both mathematical events (dice, cards) and in real world situations (the amount of time worked and the amount paid).

  • Students often confuse an independent event for a dependent event. An example of this may be that students think that the amount of time studying depends on their test score instead of their test score depends on the amount of time studying. 

OKMath Framework Introduction

Pre-Algebra Introduction

 

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